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Kinematics-1D

182 Questions Start Errorless Test
All Exams Allen Advance Errorless
JEE (Main) Jan. 2025 Q1 Errorless 6. Critical Thinking MCQ
The position vector of a moving body at any instant of time is given as $\vec{r} = (5t^2\hat{i} - 5t\hat{j})m$ . The magnitude and direction of velocity at $t = 2s$ is,
A.
$5\sqrt{15} m/s$ , making an angle of $\tan^{-1}4$ , with -ve Y axis
B.
$5\sqrt{15} m/s$ , making an angle of $\tan^{-1}4$ , with +ve X axis
C.
$5\sqrt{17} m/s$ , making an angle of $\tan^{-1}4$ , with -ve Y axis
D.
$5\sqrt{17} m/s$ , making an angle of $\tan^{-1}4$ , with +ve X axis
JEE (Main) Jan. 2025 Q2 Errorless 7. Graphical Questions MCQ
The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between $t = 0$ to $t = 4s$
A.
30 m
B.
10 m
C.
13 m
D.
11 m
JEE (Main) Jan. 2024 Q3 Errorless 6. Critical Thinking MCQ
The relation between time ‘t’ and distance ‘x’ is $t = \alpha x^{2} + \beta x$ , where $\alpha$ and $\beta$ are constants. The relation between acceleration (a) and velocity (v) is
A.
$a = -2\alpha v^{3}$
B.
$a = -5\alpha v^{5}$
C.
$a = -3\alpha v^{2}$
D.
$a = -4\alpha v^{4}$
JEE (Main) Jan. 2024 Q4 Errorless 6. Critical Thinking MCQ
Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h. Velocity of train B with respect to A and velocity of ground with respect to B are (in $ms^{-1}$ )
A.
-30 and 50
B.
-50 and -30
C.
-50 and 30
D.
-50 and -30
JEE (Main) April 2024 Q5 Errorless 6. Critical Thinking MCQ
A body travels 102.5 m in $n^{th}$ second and 115.0 m in $(n+2)^{th}$ second. The acceleration is
A.
$9m/s^{2}$
B.
$6.25m/s^{2}$
C.
$12.5m/s^{2}$
D.
$5m/s^{2}$
JEE (Main) April 2024 Q6 Errorless 6. Critical Thinking MCQ
Two cars are travelling towards each other at speed of $20ms^{-1}$ each. When the cars are 300 m apart, both the drivers apply brake and the cars retard at the rate of $2ms^{-2}$ . The distance between them when they come to rest is
A.
200 m
B.
50 m
C.
100 m
D.
25 m
JEE (Main) April 2024 Q7 Errorless 6. Critical Thinking MCQ
A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is
A.
8.8 m/s
B.
10 m/s
C.
9.2 m/s
D.
8 m/s
JEE (Main) Jan. 2023 Q8 Errorless 6. Critical Thinking MCQ
A car travels a distance of 'x' with speed $v_{1}$ and then same distance 'x' with speed $v_{2}$ in the same direction. The average speed of the car is
A.
$\frac{v_{1}v_{2}}{2(v_{1}+v_{2})}$
B.
$\frac{v_{1}+v_{2}}{2}$
C.
$\frac{2x}{v_{1}+v_{2}}$
D.
$\frac{2v_{1}v_{2}}{v_{1}+v_{2}}$
JEE (Main) Jan. 2023 Q9 Errorless 6. Critical Thinking MCQ
The distance travelled by a particle is related to time t as $x = 4t^{2}$ . The velocity of the particle at t = 5s is
A.
$40ms^{-1}$
B.
$25ms^{-1}$
C.
$20ms^{-1}$
D.
$8ms^{-1}$
JEE (Main) Jan. 2023 Q10 Errorless 6. Critical Thinking MCQ
A vehicle travels 4 km with speed of 3 km/h and another 4 km with speed of 5 km/h, then its average speed is
A.
4.25 km/h
B.
3.50 km/h
C.
4.00 km/h
D.
3.75 km/h
2023 Q11 Errorless 6. Critical Thinking MCQ
A child stands on the edge of the cliff 10m above the ground and throws a stone horizontally with an initial speed of $5ms^{-1}$ . Neglecting the air resistance, the speed with which the stone hits the ground will be ____ $ms^{-1}$ (given, $g = 10ms^{-2}$ ) (JEE (Main) Jan. 2023)
A.
20
B.
15
C.
30
D.
25
JEE (Main) April 2023 Q12 Errorless 6. Critical Thinking MCQ
A ball is thrown vertically upward with an initial velocity of 150 m/s. The ratio of velocity after 3 s and 5 s is $\frac{x+1}{x}$ . The value of x is __ Take( $g = 10m/s^{2}$ )
A.
6
B.
5
C.
-5
D.
10
JEE (Main) April 2023 Q13 Errorless 6. Critical Thinking MCQ
A particle starts with an initial velocity of $10.0ms^{-1}$ along x-direction and accelerates uniformly at the rate of $2.0ms^{-2}$ . The time taken by the particle to reach the velocity of $60.0ms^{-1}$ is ____
A.
6 s
B.
3 s
C.
30 s
D.
25 s
JEE (Main) April 2023 Q14 Errorless 6. Critical Thinking MCQ
A person travels $x$ distance with velocity $v_{1}$ and then $x$ distance with velocity $v_{2}$ in the same direction. The average velocity of the person is $v$ , then the relation between $v, v_{1}$ and $v_{2}$ will be
A.
$v = v_{1} + v_{2}$
B.
$v = \frac{v_{1} + v_{2}}{2}$
C.
$\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
D.
$\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
JEE (Main) April 2023 Q15 Errorless 6. Critical Thinking MCQ
Given below are two statements Statement I : Area under velocity-time graph gives the distance travelled by the body in a given time. Statement II : Area under acceleration-time graph is equal to the change in velocity in the given time. In the light of the above statements, choose the most appropriate answer from the options given below
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
E.
If assertion is false but reason is true.
JEE (Main) April 2023 Q16 Errorless 6. Critical Thinking MCQ
The position of a particle related to time is given by $x = (5t^{2} - 4t + 5)m$ . The magnitude of velocity of the particle at t = 2s will be
A.
$10 ms^{-1}$
B.
$14 ms^{-1}$
C.
$16 ms^{-1}$
D.
$06 ms^{-1}$
JEE (Main) Jan. 2023 Q17 Errorless 7. Graphical Questions MCQ
The velocity time graph of a body moving in a straight line is shown in figure The ratio of displacement to distance travelled by the body in time 0 to 10 s is
A.
1:1
B.
1:4
C.
1:2
D.
1:3
JEE (Main) Jan. 2023 Q18 Errorless 7. Graphical Questions MCQ
Match Column-I(x-t graphs) with Column-II(v-t graphs):
Column-IColumn-II
(A)
(B)
(C)
(D)
(P)
(Q)
(R)
(S)
A.
A-Q, B-S, C-R, D-P
B.
A-P, B-Q, C-R, D-S
C.
A-Q, B-R, C-S, D-P
D.
A-P, B-R, C-S, D-Q
JEE (Main) April 2023 Q19 Errorless 7. Graphical Questions MCQ
From the v-t graph shown, the ratio of distance to displacement in 25 s of motion
A.
$\frac{3}{5}$
B.
$\frac{1}{2}$
C.
$\frac{5}{3}$
D.
1
IEF (Main) April 2023 Q20 Errorless 7. Graphical Questions MCQ
The position-time graphs for two students A and B returning from the school to their homes are shown in figure (1) A lives closer to the school (2) $B$ lives closer to the school (3) A takes lesser time to reach home (4) $A$ travels faster than $B$ (5) $B$ travels faster than $A$ Choose the correct answer from the options given below
A.
1 and 5 only
B.
2 and 5 only
C.
1, 3 and 5 only
D.
1, 3 and 4 only
JEE (Main) June 2022 Q21 Errorless 6. Critical Thinking MCQ
When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is
A.
19.6 m
B.
29.4 m
C.
39.2 m
D.
73.5 m
JEE (Main) June 2022 Q22 Errorless 6. Critical Thinking MCQ
An object of mass 5kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to [Use $g = 10 ms^{-2}$ ]
A.
1:1
B.
$\sqrt{2} : \sqrt{3}$
C.
$\sqrt{3} : \sqrt{2}$
D.
2:3
JEE (Main) June 2022 Q23 Errorless 6. Critical Thinking MCQ
An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero
A.
Momentum
B.
Potential energy
C.
Acceleration
D.
Force
JEE (Main) June 2022 Q24 Errorless 6. Critical Thinking MCQ
A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s., the distance travelled by the toy in the next t s will be
A.
10 m
B.
20 m
C.
30 m
D.
40 m
JEE (Main) June 2022 Q25 Errorless 6. Critical Thinking MCQ
Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_{P}(t) = \alpha t + \beta t^{2}$ and $X_{Q}(t) = ft - t^{2}$ . At what time, both the buses have same velocity
A.
$\frac{\alpha - f}{1 + \beta}$
B.
$\frac{\alpha + f}{2(\beta - 1)}$
C.
$\frac{\alpha + f}{2(1 + \beta)}$
D.
$\frac{f - \alpha}{2(1 + \beta)}$