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Motion in 1D

108 Questions Start DPT Test
All Exams Objective Physics Vol-1 DPT
Q1 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Distance is the total length of the path covered by an object during its motion, regardless of the direction of travel. It is a scalar quantity and is calculated by adding the individual path lengths traversed in each step of the journey.
A scooter is moving along a straight line $AB$ covers a distance of $360\text{ m}$ in $24\text{ s}$ and returns back from $B$ to $C$ and covers $240\text{ m}$ in $18\text{ s}$. Find the total distance travelled by the scooter.
A.
$120\text{ m}$
B.
$600\text{ m}$
C.
$360\text{ m}$
D.
$240\text{ m}$
Q2 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: When a circular wheel rolls without slipping, the total distance covered in $n$ revolutions is equal to $n$ times the circumference of the wheel. The circumference of a circle is given by $\pi d$, where $d$ is the diameter of the wheel.
A wheel completes $2000\text{ revolutions}$ to cover the $9.5\text{ km}$ distance. Find the diameter of the wheel.
A.
$1.51\text{ m}$
B.
$3.02\text{ m}$
C.
$0.75\text{ m}$
D.
$2.14\text{ m}$
Q3 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Distance is the total path length traversed by a body, regardless of direction. Displacement is the shortest straight-line distance vector from the initial position to the final position, which can be evaluated using vector addition or right-angled triangle geometry (Pythagoras theorem).
A man starts from his home and walks $50\text{ m}$ towards north, then he turns towards east and walks $40\text{ m}$ and then reaches to his office after moving $20\text{ m}$ towards south. What is the total distance covered by the man from his home to office and what is his displacement from his home to office?
A.
Distance = $110\text{ m}$, Displacement = $50\text{ m}$
B.
Distance = $50\text{ m}$, Displacement = $110\text{ m}$
C.
Distance = $110\text{ m}$, Displacement = $70\text{ m}$
D.
Distance = $70\text{ m}$, Displacement = $50\text{ m}$
Q4 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Distance is the actual length of the path traversed by an object, while displacement is the shortest straight-line distance from its initial position to its final position. For motion along a circular path, distance is calculated as a fraction of the circle's circumference, and displacement is calculated using the straight-line chord length connecting the initial and final positions.
An object covers $1/4\text{th}$ of a circular path of radius $r$. What will be the ratio of the distance and displacement of the object?
A.
$\frac{\pi}{2\sqrt{2}}$
B.
$\frac{\pi}{\sqrt{2}}$
C.
$\frac{2\sqrt{2}}{\pi}$
D.
$\frac{\pi}{4}$
Q5 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: For motion along a semicircular path, the displacement between the initial and final points is equal to the diameter of the path ($2r$). The distance travelled is the actual path length along the semicircle, which is equal to half of the circumference ($\pi r$).
Displacement of a person moving from $X$ to $Y$ along a semicircular path of radius $r$ is $200\text{ m}$. What is the distance travelled by him?
A.
$200\text{ m}$
B.
$100\pi\text{ m}$
C.
$400\text{ m}$
D.
$200\pi\text{ m}$
Q6 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Distance is the total actual path length covered during motion, which for circular motion depends on the number of completed revolutions multiplied by the circumference ($2\pi r$ or $\pi D$). Displacement is the shortest distance between the initial position and the final position. For an integer number of full rounds, displacement is zero, while for a half round, displacement is equal to the diameter of the track.
An athlete completes one round of a circular track of diameter $200\text{ m}$ in $40\text{ s}$. What will be the distance covered and the displacement at the end of $2\text{ min } 20\text{ s}$?
A.
Distance = $2200\text{ m}$, Displacement = $200\text{ m}$
B.
Distance = $200\text{ m}$, Displacement = $2200\text{ m}$
C.
Distance = $4400\text{ m}$, Displacement = $100\text{ m}$
D.
Distance = $2200\text{ m}$, Displacement = $0\text{ m}$
Q7 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: One-dimensional motion is the motion of a body along a straight line path. In such motion, only one coordinate is required to specify the position of the object at any instant of time.
Which of the following is a one-dimensional motion?
A.
Landing of an aircraft
B.
Earth revolving around the sun
C.
Motion of wheels of moving train
D.
Train running on a straight track
Q8 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: The distance of a point from the origin (or starting point) in three-dimensional space is given by the magnitude of the displacement vector. When an object moves along three mutually perpendicular directions (X, Y, and Z axes), the net direct distance from the initial position is calculated using the 3D distance formula: $d = \sqrt{x^2 + y^2 + z^2}$.
A person moves towards east for $3\text{ m}$, then towards north for $4\text{ m}$ and then moves upwards for $5\text{ m}$. What is his distance now from the starting point?
A.
$10\text{ m}$
B.
$12\text{ m}$
C.
$5\sqrt{2}\text{ m}$
D.
$5\text{ m}$
Q9 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Distance along a circular arc is equal to the product of the radius of the circle and the angle subtended by the arc at the center measured in radians ($\text{Distance} = R \times \theta$). To convert an angle from degrees to radians, multiply by $\frac{\pi}{180^{\circ}}$.
A particle moves in a circle of radius $R$ from $A$ to $B$ as shown in figure. The distance covered by the object is image.png
A.
$\frac{\pi R}{3}$
B.
$\frac{\pi R}{2}$
C.
$\frac{\pi R}{4}$
D.
$\pi R$
Q10 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: When a wheel rolls forward by half a revolution without slipping, its center moves horizontally by a distance equal to half of its circumference ($\pi R$). Simultaneously, the point initially in contact with the ground moves from the bottom position to the top position of the wheel, resulting in a vertical displacement equal to the diameter of the wheel ($2R$). The net displacement magnitude is the straight-line distance calculated using the Pythagorean theorem: $d = \sqrt{(\pi R)^2 + (2R)^2}$.
A wheel of radius $1\text{ m}$ rolls forward half a revolution on a horizontal ground. The magnitude of displacement of the point of the wheel initially in contact with the ground is
A.
$2\pi$
B.
$\sqrt{2}\pi$
C.
$\sqrt{\pi^2 + 4}$
D.
$\pi$
Q11 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Displacement ($\Delta x$) on a straight line is defined as the final position ($x_f$) minus the initial position ($x_i$), given by $\Delta x = x_f - x_i$. Displacement is negative when the final position lies to the left of the initial position ($x_f < x_i$).
The three initial and final positions of a man on the x-axis are given as:
(i) $(-8\text{ m}, 7\text{ m})$
(ii) $(7\text{ m}, -3\text{ m})$
(iii) $(-7\text{ m}, 3\text{ m})$
Which pair gives the negative displacement?
A.
(i)
B.
(ii)
C.
(iii)
D.
(i) and (iii)
Q12 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Displacement is the shortest straight-line distance between the initial and final positions of an object, while distance is the total length of the actual path traversed. Since displacement cannot exceed the total path length, displacement is always less than or equal to distance. Therefore, the ratio of displacement to distance is always less than or equal to one (equal to one for unidirectional motion in a straight line).
The numerical ratio of displacement to the distance for a moving object is always
A.
less than one
B.
equal to one
C.
equal to or less than one
D.
equal to or greater than one
Q13 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Distance is the actual length of the path traversed by a particle, which for half a revolution of a circular path is equal to half of the circumference ($\pi r$). Displacement is the shortest straight-line distance from the initial position to the final position, which for a half revolution is equal to the diameter of the circular path ($2r$).
A particle moves along a circular path of radius $r$. The distance and displacement of the particle after half a revolution is
A.
$0, 2\pi r$
B.
$2\pi r, 0$
C.
$0, \pi r$
D.
$\pi r, 0$
Q14 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Distance (total path length covered) and Displacement (shortest distance between initial and final position, i.e., final position minus initial position).
A particle starts from the origin, goes along $X$-axis to the point $(20\text{ m}, 0)$ and then returns along the same line to the point $(-20\text{ m}, 0)$. The distance and displacement of the particle during the trip are
A.
$40\text{ m}, 0$
B.
$40\text{ m}, -20\text{ m}$
C.
$60\text{ m}, -20\text{ m}$
D.
$40\text{ m}, 20\text{ m}$
Q15 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed, defined as the total distance traveled divided by the total time taken.
Abdul while driving to school computes the average speed for his trip to be $20\text{ km h}^{-1}$. On his return trip along the same route, there is less traffic and the average speed is $40\text{ km h}^{-1}$. What is the average speed for Abdul's trip?
A.
$30.5\text{ km h}^{-1}$
B.
$26.67\text{ km h}^{-1}$
C.
$24.5\text{ km h}^{-1}$
D.
$32.0\text{ km h}^{-1}$
Q16 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed when the distance is split into equal halves travelled at different constant speeds, calculated using the harmonic mean of the speeds.
A car covers the first half of the distance between two places at a speed of $40\text{ km h}^{-1}$ and second half at $60\text{ km h}^{-1}$. Calculate the average speed of the car.
A.
$52\text{ km h}^{-1}$
B.
$45\text{ km h}^{-1}$
C.
$48\text{ km h}^{-1}$
D.
$50\text{ km h}^{-1}$
Q17 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed for a round trip with two different speeds over equal distances, calculated as the harmonic mean of the speeds.
A car moves from $X$ to $Y$ with a uniform speed $v_u$ and returns to $X$ with a uniform speed $v_d$. Find average speed for this round trip.
A.
$\frac{v_u v_d}{v_u + v_d}$
B.
$\frac{3v_u v_d}{v_u + v_d}$
C.
$\frac{2v_u v_d}{v_u + v_d}$
D.
$\frac{v_u + v_d}{2v_u v_d}$
Q18 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed, defined as the total distance traveled divided by the total time taken for a journey with varying segments of speed and time.
A particle travelled half the distance with a speed $v_0$. The remaining part of the distance was covered with speed $v_1$ for half the time and with speed $v_2$ for the other half of the time. Find the average speed of the particle.
A.
$\frac{2v_0(v_1 + v_2)}{v_1 + v_2 + v_0}$
B.
$\frac{2v_0(v_1 + v_2)}{v_1 + v_2 + 2v_0}$
C.
$\frac{v_0(v_1 + v_2)}{2(v_1 + v_2 + v_0)}$
D.
$\frac{v_0(v_1 + v_2)}{v_1 + v_2 + v_0}$
Q19 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average velocity, defined as the ratio of total displacement to the total time taken for the motion.
In one second, a particle goes from point $A$ to point $B$ moving in a semicircular path as shown in figure. Find the magnitude of average velocity. image.png
A.
$1.5\text{ ms}^{-1}$
B.
$2.5\text{ ms}^{-1}$
C.
$2\text{ ms}^{-1}$
D.
$3\text{ ms}^{-1}$
Q20 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Distance as total path length ($AB + BC + CD$) and Displacement as the shortest straight-line distance from initial to final position using vector components.
A farmer has to go $500\text{ m}$ due north, $400\text{ m}$ due east and $200\text{ m}$ due south to reach his field. If he takes $20\text{ min}$ to reach the field, (i) what distance has he to walk to reach the field? (ii) what is the displacement from his house to the field? (iii) what is the average speed of farmer during the walk? (iv) what is the average velocity of farmer during the walk? [Note: This question specifically focuses on finding the total distance and magnitude of displacement.]
A.
Distance: $1100\text{ m}$, Displacement: $500\text{ m}$
B.
Distance: $1000\text{ m}$, Displacement: $400\text{ m}$
C.
Distance: $1100\text{ m}$, Displacement: $600\text{ m}$
D.
Distance: $900\text{ m}$, Displacement: $500\text{ m}$
Q21 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed defined as total distance divided by total time, and average velocity defined as net displacement divided by total time.
Joseph jogs from one end $A$ to the other end $B$ of a straight $300\text{ m}$ road in $2\text{ min } 50\text{ s}$ and then turns around and jogs $100\text{ m}$ back to point $C$ in another $1\text{ min}$. What are Joseph's average speeds and velocities in jogging (i) from $A$ to $B$ and (ii) from $A$ to $C$?
A.
Average speed from $A$ to $B$ is $1.76\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $1.76\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $1.74\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $0.87\text{ ms}^{-1}$
B.
Average speed from $A$ to $B$ is $1.50\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $1.50\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $1.20\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $0.50\text{ ms}^{-1}$
C.
Average speed from $A$ to $B$ is $2.00\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $2.00\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $1.90\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $1.10\text{ ms}^{-1}$
D.
Average speed from $A$ to $B$ is $1.76\text{ ms}^{-1}$, average velocity from $A$ to $B$ is $1.76\text{ ms}^{-1}$; Average speed from $A$ to $C$ is $2.10\text{ ms}^{-1}$, average velocity from $A$ to $C$ is $1.50\text{ ms}^{-1}$
Q22 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Finding instantaneous position from a given position-time equation, calculating displacement as the difference between final and initial positions, and average velocity as displacement divided by the time interval.
The position of an object moving along $X$-axis is given by $x = 3t - 4t^2 + t^3$, where $x$ is in metres and $t$ in seconds. Find the position of the object at $t = 2\text{ s}$ and $t = 4\text{ s}$. What is the object displacement between $t = 0\text{ s}$ and $t = 4\text{ s}$, and what is its average velocity for the time interval from $t = 2\text{ s}$ to $t = 4\text{ s}$?
A.
$x_2 = -2\text{ m}$, $x_4 = 12\text{ m}$, Displacement = $12\text{ m}$, Average Velocity = $7\text{ ms}^{-1}$
B.
$x_2 = 2\text{ m}$, $x_4 = 10\text{ m}$, Displacement = $10\text{ m}$, Average Velocity = $5\text{ ms}^{-1}$
C.
$x_2 = -4\text{ m}$, $x_4 = 14\text{ m}$, Displacement = $14\text{ m}$, Average Velocity = $8\text{ ms}^{-1}$
D.
$x_2 = -2\text{ m}$, $x_4 = 15\text{ m}$, Displacement = $15\text{ m}$, Average Velocity = $9\text{ ms}^{-1}$
Q23 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed for a journey when time is divided into equal intervals with different constant speeds, calculated as the arithmetic mean of the speeds.
A car has to cover the distance $60\text{ km}$. If half of the total time, it travels with speed $80\text{ km h}^{-1}$ and in rest half time, its speed becomes $40\text{ km h}^{-1}$, the average speed of car will be
A.
$120\text{ km h}^{-1}$
B.
$80\text{ km h}^{-1}$
C.
$60\text{ km h}^{-1}$
D.
$180\text{ km h}^{-1}$
Q24 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed, defined as the total distance traveled divided by the total time taken for the trip.
During the first $18\text{ min}$ of a $60\text{ min}$ trip, a car has an average speed of $11\text{ m min}^{-1}$. What should be the average speed for remaining $42\text{ min}$, so that car is having an average speed of $21\text{ m min}^{-1}$ for the entire trip?
A.
$25.3\text{ m min}^{-1}$
B.
$29.2\text{ m min}^{-1}$
C.
$31\text{ m min}^{-1}$
D.
$35.6\text{ m min}^{-1}$
Q25 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average speed, defined as the total distance traveled divided by the total time taken for the specified time interval.
A man walks on a straight road from his home to a market $2.5\text{ km}$ away with a speed of $5\text{ km h}^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5\text{ km h}^{-1}$. The average speed of the man over the interval of time $0$ to $40\text{ min}$ is equal to
A.
$5\text{ km h}^{-1}$
B.
$\frac{25}{4}\text{ km h}^{-1}$
C.
$\frac{30}{4}\text{ km h}^{-1}$
D.
$\frac{45}{8}\text{ km h}^{-1}$
Q26 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Distance, displacement, average speed, and average velocity definitions for linear motion.
A particle is constrained to move on a straight line path. It returns to the starting point after $10\text{ s}$. The total distance covered by the particle during this time is $30\text{ m}$. Which of the following statements about the motion of the particle is true?
A.
Displacement of the particle is zero
B.
Average speed of the particle is $3\text{ ms}^{-1}$
C.
Displacement of the particle is $30\text{ m}$
D.
Both (a) and (b)
Q27 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Uniform speed and distance travelled. The total distance covered by a train to completely cross a bridge is the sum of the length of the train and the length of the bridge.
A $150\text{ m}$ long train is moving with a uniform velocity of $45\text{ km h}^{-1}$. The time taken by the train to cross a bridge of length $850\text{ m}$ is
A.
$56\text{ s}$
B.
$68\text{ s}$
C.
$80\text{ s}$
D.
$92\text{ s}$
Q28 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average velocity, defined as total displacement divided by total time taken.
An insect crawls a distance of $4\text{ m}$ along north in $10\text{ s}$ and then a distance of $3\text{ m}$ along east in $5\text{ s}$. The average velocity of the insect is
A.
$\frac{7}{15}\text{ ms}^{-1}$
B.
$\frac{1}{5}\text{ ms}^{-1}$
C.
$\frac{1}{3}\text{ ms}^{-1}$
D.
$\frac{4}{5}\text{ ms}^{-1}$
Q29 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average velocity defined as the total displacement divided by the total time taken.
A particle traversed $\frac{3}{4}\text{th}$ of the circle of radius $R$ in time $t$. The magnitude of the average velocity of the particle in this time interval is
A.
$\frac{\pi R}{t}$
B.
$\frac{3\pi R}{2t}$
C.
$\frac{R\sqrt{2}}{t}$
D.
$\frac{R}{\sqrt{2}t}$
Q30 Objective Physics Vol-1 Basic Concepts of Motion MCQ
24 Jul 2026
Concept: Kinematics - Average velocity along a semicircular path, defined as the displacement (diameter of the semicircle) divided by the time taken to cover the semicircular arc.
A boy is running over a circular track with uniform speed of $10\text{ ms}^{-1}$. What is the average velocity for movement of boy along semicircle (in $\text{ms}^{-1}$)?
A.
$\frac{10}{\pi}$
B.
$\frac{40}{\pi}$
C.
$10$
D.
$\frac{20}{\pi}$
Q31 DPT DPT-1 MCQ
25 Jul 2026
Concept: Displacement is a vector quantity defined as the shortest distance between the initial position and the final position. When a body moves in three mutually perpendicular directions, the magnitude of the net displacement vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ is given by $r = \sqrt{x^2 + y^2 + z^2}$.
A body moves $6\text{ m}$ north, $8\text{ m}$ east and $10\text{ m}$ vertically upwards. What is its resultant displacement from initial position?
A.
$10\sqrt{2}\text{ m}$
B.
$10\text{ m}$
C.
$\frac{10}{\sqrt{2}}\text{ m}$
D.
$10 \times 2\text{ m}$
Q32 DPT DPT-1 MCQ
25 Jul 2026
Concept: Displacement is a vector quantity representing the shortest straight-line distance from the initial position to the final position. When two displacement vectors are perpendicular to each other, the magnitude of the resultant displacement vector $\vec{r} = x\hat{i} + y\hat{j}$ is calculated using the Pythagorean theorem: $r = \sqrt{x^2 + y^2}$.
A man goes $10\text{ m}$ towards North, then $20\text{ m}$ towards east then displacement is
A.
$30\text{ m}$
B.
$25.5\text{ m}$
C.
$22.5\text{ m}$
D.
$25\text{ m}$
Q33 DPT DPT-1 MCQ
25 Jul 2026
Concept: Displacement is a vector quantity representing the shortest path from the initial to the final position. A motion in a plane can be broken down into orthogonal vector components along the East-West (x-axis) and North-South (y-axis) directions. The total displacement is the vector sum of individual displacement vectors $\vec{r} = \vec{r}_1 + \vec{r}_2 + \vec{r}_3 = x\hat{i} + y\hat{j}$.
A person moves $30\text{ m}$ north and then $20\text{ m}$ towards east and finally $30\sqrt{2}\text{ m}$ in south-west direction. The displacement of the person from the origin will be
A.
$10\text{ m}$ along north
B.
$10\text{ m}$ along south
C.
$10\text{ m}$ along west
D.
Zero
Q34 DPT DPT-1 MCQ
25 Jul 2026
Concept: Displacement is a vector quantity defined as the shortest distance from the initial position to the final position. In three-dimensional space, the net displacement vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ is obtained by summing the individual vector displacements along mutually perpendicular axes. The magnitude of the displacement vector is given by $r = \sqrt{x^2 + y^2 + z^2}$.
An aeroplane flies $400\text{ m}$ north and $300\text{ m}$ south and then flies $1200\text{ m}$ upwards then net displacement is
A.
$1400\text{ m}$
B.
$1200\text{ m}$
C.
$1300\text{ m}$
D.
$1500\text{ m}$
Q35 DPT DPT-1 MCQ
25 Jul 2026
Concept: Displacement is a vector quantity defined as the shortest straight-line distance from the initial position to the final position. For motion along a circular path, completing one full revolution brings the object back to its starting point, resulting in zero displacement for that complete turn. If an object stops at a diametrically opposite point after a fractional revolution, the magnitude of the displacement is equal to the diameter of the circular track ($2R$).
An athlete completes one round of a circular track of radius $R$ in $40\text{ sec}$. What will be his displacement at the end of $2\text{ min } 20\text{ sec}$?
A.
$2\pi R$
B.
$7\pi R$
C.
$2R$
D.
Zero
Q36 DPT DPT-1 MCQ
25 Jul 2026
Concept: When a circular wheel rolls forward without slipping, the point initially in contact with the ground undergoes both horizontal translation and vertical motion. During half a revolution, the horizontal displacement of the point is equal to half the circumference of the wheel ($\pi r$), and its vertical displacement from the bottom to the top position is equal to the diameter of the wheel ($2r$). The net displacement magnitude is calculated using the Pythagorean theorem: $S = \sqrt{x^2 + y^2}$.
A wheel of radius $1\text{ meter}$ rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is
A.
$2\pi$
B.
$\sqrt{2}\pi$
C.
$\sqrt{\pi^2 + 4}$
D.
$\pi$
Q37 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average velocity is defined as the total displacement divided by the total time taken. When a journey is divided into equal distance intervals covered at different uniform speeds, the average velocity is given by the harmonic mean of the speeds.
A person travels along a straight road for half the distance with velocity $v_1$ and the remaining half distance with velocity $v_2$. The average velocity is given by
A.
$v_1 v_2$
B.
$\frac{v_2^2}{v_1^2}$
C.
$\frac{v_1 + v_2}{2}$
D.
$\frac{2 v_1 v_2}{v_1 + v_2}$
Q38 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as the total distance covered divided by the total time taken. When a body travels equal distances at two different speeds $v_1$ and $v_2$, the average speed is given by the harmonic mean of the two speeds: $v_{av} = \frac{2 v_1 v_2}{v_1 + v_2}$.
A car travels from $A$ to $B$ at a speed of $20\text{ km/hr}$ and returns at a speed of $30\text{ km/hr}$. The average speed of the car for the whole journey is
A.
$25\text{ km/hr}$
B.
$24\text{ km/hr}$
C.
$50\text{ km/hr}$
D.
$5\text{ km/hr}$
Q39 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as the total distance covered divided by the total time taken for the journey. When a body covers equal distances for the forward and return journeys at different uniform speeds $v_1$ and $v_2$, the average speed is given by $v_{av} = \frac{2 v_1 v_2}{v_1 + v_2}$.
A boy walks to his school at a distance of $6\text{ km}$ with constant speed of $2.5\text{ km/hr}$ and walks back with a constant speed of $4\text{ km/hr}$. His average speed for round trip expressed in $\text{km/hour}$ is
A.
$3$
B.
$1/2$
C.
$24/13$
D.
$40/13$
Q40 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as the total distance covered divided by the total time taken for the journey. When a journey is divided into two equal distances covered at different uniform speeds $v_1$ and $v_2$, the average speed is given by the harmonic mean of the speeds: $v_{av} = \frac{2 v_1 v_2}{v_1 + v_2}$.
A car travels the first half of a distance between two places at a speed of $30\text{ km/hr}$ and the second half of the distance at $50\text{ km/hr}$. The average speed of the car for the whole journey is
A.
$40.0\text{ km/hr}$
B.
$42.5\text{ km/hr}$
C.
$37.5\text{ km/hr}$
D.
$35.0\text{ km/hr}$
Q41 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as the total distance covered divided by the total time taken for the trip. When a journey is divided into unequal distance segments traveled at different constant speeds, the total time is calculated by summing the time taken for each segment $t_i = \frac{s_i}{v_i}$. The average speed is then $v_{av} = \frac{S}{T_{total}}$.
One car moving on a straight road covers one third of the distance with $20\text{ km/hr}$ and the rest with $60\text{ km/hr}$. The average speed is
A.
$40\text{ km/hr}$
B.
$36\text{ km/hr}$
C.
$46\frac{2}{3}\text{ km/hr}$
D.
$80\text{ km/hr}$
Q42 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as total distance divided by total time elapsed. When a body moves with uniform speed $v_1$ for time $t_1$ and uniform speed $v_2$ for time $t_2$, the average speed is given by the time-weighted average $v_{av} = \frac{v_1 t_1 + v_2 t_2}{t_1 + t_2}$. When the time intervals are equal ($t_1 = t_2 = \frac{t}{2}$), the average speed simplifies to the arithmetic mean of the speeds: $v_{av} = \frac{v_1 + v_2}{2}$.
A car moves for half of its time at $80\text{ km/h}$ and for rest half of time at $40\text{ km/h}$. Total distance covered is $60\text{ km}$. What is the average speed of the car?
A.
$60\text{ km/h}$
B.
$80\text{ km/h}$
C.
$120\text{ km/h}$
D.
$180\text{ km/h}$
Q43 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as the ratio of total distance traveled to total time taken. When a body moves with different speeds over different time intervals, the individual distances covered are calculated as $d = v \times t$. The average speed is then calculated using $v_{av} = \frac{d_1 + d_2}{t_1 + t_2}$.
A train has a speed of $60\text{ km/h}$ for the first one hour and $40\text{ km/h}$ for the next half hour. Its average speed in $\text{km/h}$ is
A.
$50$
B.
$53.33$
C.
$48$
D.
$70$
Q44 DPT DPT-1 MCQ
25 Jul 2026
Concept: When a train crosses an object with a non-negligible length, such as a bridge, the total distance covered by the train to completely cross it is equal to the sum of the length of the train and the length of the bridge ($D = L_{train} + L_{bridge}$). The speed is converted from $\text{km/h}$ to $\text{m/s}$ using the conversion factor $1\text{ km/h} = \frac{5}{18}\text{ m/s}$, and the time required is determined using $t = \frac{D}{v}$.
A $150\text{ m}$ long train is moving with a uniform velocity of $45\text{ km/h}$. The time taken by the train to cross a bridge of length $850\text{ meters}$ is
A.
$56\text{ sec}$
B.
$68\text{ sec}$
C.
$80\text{ sec}$
D.
$92\text{ sec}$
Q45 DPT DPT-1 MCQ
25 Jul 2026
Concept: Displacement is a vector quantity defined as the net change in position from the starting point to the ending point. If an object returns to its initial position, its total displacement is zero regardless of the distance traveled. Average speed is a scalar quantity calculated as total distance divided by total time: $v_{av} = \frac{\text{Total distance}}{\text{Total time}}$.
A particle is constrained to move on a straight line path. It returns to the starting point after $10\text{ sec}$. The total distance covered by the particle during this time is $30\text{ m}$. Which of the following statements about the motion of the particle is false?
A.
Displacement of the particle is zero
B.
Average speed of the particle is $3\text{ m/s}$
C.
Displacement of the particle is $30\text{ m}$
D.
Both (a) and (b)
Q46 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as the total distance covered divided by the total time taken ($v_{av} = \frac{\text{Total distance}}{\text{Total time}}$). When calculating average speed over a specific time interval, one must determine the position and distance traveled up to that exact time limit by considering the separate legs of the motion.
A man walks on a straight road from his home to a market $2.5\text{ km}$ away with a speed of $5\text{ km/h}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5\text{ km/h}$. The average speed of the man over the interval of time $0$ to $40\text{ min}$ is equal to
A.
$\frac{30}{4}\text{ km/h}$
B.
$5\text{ km/h}$
C.
$\frac{25}{4}\text{ km/h}$
D.
$\frac{45}{8}\text{ km/h}$
Q47 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average velocity is defined as total displacement divided by total time ($\vec{v}_{av} = \frac{\Delta\vec{r}}{\Delta t}$), while average speed is defined as total distance divided by total time ($v_{av} = \frac{\Delta s}{\Delta t}$). Since distance is always greater than or equal to the magnitude of displacement ($\text{Distance} \ge \vert{}\text{Displacement}\vert{}$), the magnitude of average velocity is always less than or equal to the average speed. Therefore, the ratio of average velocity to average speed is unity or less ($\le 1$).
The ratio of the numerical values of the average velocity and average speed of a body is always
A.
Unity
B.
Unity or less
C.
Unity or more
D.
Less than unity
Q48 DPT DPT-1 MCQ
25 Jul 2026
Concept: Mean (or average) velocity is defined as total displacement divided by total time elapsed. When a body moves along a straight path with different uniform velocities for equal time intervals ($t_1 = t_2 = \frac{T}{2}$), the mean velocity is given by the arithmetic mean of the individual velocities: $V = \frac{v_1 + v_2}{2}$.
A person travels along a straight road for the first half time with a velocity $v_1$ and the next half time with a velocity $v_2$. The mean velocity $V$ of the man is
A.
$\frac{2}{V} = \frac{1}{v_1} + \frac{1}{v_2}$
B.
$V = \frac{v_1 + v_2}{2}$
C.
$V = \sqrt{v_1 v_2}$
D.
$V = \sqrt{\frac{v_1}{v_2}}$
Q49 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average speed is defined as the total distance covered divided by the total time taken for the trip. When a journey is divided into distance fractions $f_1$ and $f_2$ covered at speeds $v_1$ and $v_2$ respectively, the total time is calculated by adding the time taken for each fraction: $T = \frac{f_1 S}{v_1} + \frac{f_2 S}{v_2}$. Average speed is then given by $v_{av} = \frac{S}{T}$.
If a car covers $2/5$ of the total distance with $v_1$ speed and $3/5$ distance with $v_2$ then average speed is
A.
$\frac{1}{2}\sqrt{v_1 v_2}$
B.
$\frac{v_1 + v_2}{2}$
C.
$\frac{2 v_1 v_2}{v_1 + v_2}$
D.
$\frac{5 v_1 v_2}{3 v_1 + 2 v_2}$
Q50 DPT DPT-1 MCQ
25 Jul 2026
Concept: Average velocity is defined as the total displacement divided by the total time taken. When a body moves with velocities $v_1, v_2, \dots, v_n$ for equal intervals of time ($t_1 = t_2 = \dots = t_n = t$), the average velocity simplifies to the arithmetic mean of the individual velocities: $v_{av} = \frac{v_1 + v_2 + \dots + v_n}{n}$.
A particle moves for $20\text{ seconds}$ with velocity $3\text{ m/s}$ and then velocity $4\text{ m/s}$ for another $20\text{ seconds}$ and finally moves with velocity $5\text{ m/s}$ for next $20\text{ seconds}$. What is the average velocity of the particle?
A.
$3\text{ m/s}$
B.
$4\text{ m/s}$
C.
$5\text{ m/s}$
D.
$\text{Zero}$