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Kinematics-1D

538 Questions Start Allen Test
All Exams Allen Advance Errorless
IIT-JEE 1993 Q101 Advance ARCHIVE: JEE ADVANCED MCQ
A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t=0. At this instant of time, the horizontal component of its velocity is v. A bead Q of same mass as P is ejected from A at t=0 along the horizontal string AB, with a speed v. Friction between the bead and the string may be neglected. Let $t_{P}$ and $t_{Q}$ be the respective times taken by P and Q to reach the point B, then
A.
$t_{P} < t_{Q}$
B.
$t_{P}=t_{Q}$
C.
$t_{P} > t_{Q}$
D.
$\frac{t_{\mathrm{P}}}{t_{\mathrm{Q}}} = \frac{\text{length of arc } ACB}{\text{length of chord } AB}$
IIT-JEE 1993 Q102 Advance ARCHIVE: JEE ADVANCED MSQ
A particle of mass m moves on the x-axis as follows: it starts from rest at t=0 from the point x=0 and comes to rest at t=1 at the point x=1. No other information is available about its motion at intermediate time $\text{(0t1)}$ . If $\alpha$ denotes the instantaneous acceleration of the particle, then
A.
$\alpha$ cannot remain positive for all $t$ in the interval $0 \leq t \leq 1$
B.
$|\alpha|$ cannot exceed 2 at any point in its path
C.
$|\alpha|$ must be $\geq 4$ at some point or points in its path
D.
$\alpha$ must change sign during the motion but no other assertion can be made with the information given
NCERT 1990 Basic Level Q103 Errorless Distance and Displacement MCQ
An athlete completes one round of a circular track of radius R in 40 seconds. What will be his displacement at the end of 2 minutes 20 seconds
A.
Zero
B.
2R
C.
$2\pi R$
D.
$7\pi R$
NCERT 1990 Basic Level Q104 Errorless Acceleration MCQ
The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is
A.
Increasing with time
B.
Decreasing with time
C.
Constant but not zero
D.
Zero
CBSE PMT 1989 Basic Level Q105 Errorless Speed and Velocity MCQ
A car travels a distance of 2000 m. If the first half distance is covered at 40 km/hour and the second half with speed v and the average speed is 48 km/hour, then the value of v is
A.
56 km/hour
B.
60 km/hour
C.
50 km/hour
D.
48 km/hour
IIT-JEE 1988 Q106 Advance ARCHIVE: JEE ADVANCED MCQ
A boat which has a speed of $5\mathrm{kmh}^{-1}$ in still water crosses a river of width $1\mathrm{km}$ along the shortest possible path in 15 minute. The velocity of the river water in $\mathrm{kmh}^{-1}$ is
A.
1
B.
3
C.
4
D.
$\sqrt{41}$
MNR 1987; MP PET 1996 Basic Level Q107 Errorless Speed and Velocity MCQ
A particle moves along x-axis in such a way that its coordinate x varies with time t according to the equation $x = (2 - 5t + 6t^{2})m$ . The initial velocity of the particle is
A.
-5 m/s
B.
6 m/s
C.
-3 m/s
D.
3 m/s
CPMT 1986 Basic Level Q108 Errorless Position Time Graph MCQ
The graph between the displacement x and time t for a particle moving in a straight line is shown in figure. During the interval OA, AB, BC and CD, the acceleration of the particle is OA AB BC CD
A.
OA-+, AB-ā—‹, BC-+, CD-+
B.
OA-+, AB-ā—‹, BC-+, CD-ā—‹
C.
OA-+, AB-ā—‹, BC-āˆ’, CD-+
D.
OA-āˆ’, AB-ā—‹, BC-āˆ’, CD-ā—‹
MNR 1986 Basic Level Q109 Errorless Motion Under Gravity MCQ
A man in a balloon rising vertically with an acceleration of $4.9 \, m/sec^{2}$ releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reached by the ball is $(g = 9.8 \, m/sec^{2})$
A.
14.7 m
B.
19.6 m
C.
9.8 m
D.
24.5 m
IIT-JEE 1983 Q110 Advance ARCHIVE: JEE ADVANCED MCQ
A river is flowing from west to east at a speed of 5 m per minute. A man on the south bank of the river, capable of swimming at 10 m per minute in still water wants to swim across the river to a point directly opposite in the shortest time. He should then swim in a direction
A.
$$<br /> 6 0 ^ {\circ}<br /> $$west of north
B.
$30^{\circ}$ east of north
C.
$30^{\circ}$ west of north
D.
$60^{\circ}$ east of north
IIT-JEE 1982 Q111 Advance ARCHIVE: JEE ADVANCED MCQ
In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed
A.
$2U\cos \theta$
B.
$\frac{U}{\cos\theta}$
C.
$\frac{2U}{\cos\theta}$
D.
$U \cos \theta$
IIT-JEE 1982 Q112 Advance ARCHIVE: JEE ADVANCED MCQ
A particle is moving Eastwards with a velocity of $5 \, ms^{-1}$ . In 10 s, the velocity changes to $5 \, ms^{-1}$ Northwards. The average acceleration in this time is
A.
zero
B.
$\frac{1}{\sqrt{2}} \, ms^{-2}$ towards North-East
C.
$\frac{1}{\sqrt{2}} \, ms^{-2}$ towards North-West
D.
$\frac{1}{2} \, ms^{-2}$ towards North
NCERT 1982 Advance Level Q113 Errorless Equation of Kinematics (uniform Acceleration) MCQ
A point moves with uniform acceleration and $v_{1}, v_{2}$ and $v_{3}$ denote the average velocities in the three successive intervals of time $t_{1}, t_{2}$ and $t_{3}$ . Which of the following relations is correct
A.
$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}-t_{2}):(t_{2}+t_{3})$
B.
$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}+t_{2}):(t_{2}+t_{3})$
C.
$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}-t_{2}):(t_{1}-t_{3})$
D.
$(v_{1}-v_{2}):(v_{2}-v_{3})=(t_{1}-t_{2}):(t_{2}-t_{3})$
NCERT 1981 Basic Level Q114 Errorless Motion Under Gravity MCQ
A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time t/2 sec
A.
At h/2 from the ground
B.
At h/4 from the ground
C.
Depends upon mass and volume of the body
D.
At $3h / 4$ from the ground
NCERT 1971 Basic Level Q115 Errorless Position Time Graph MCQ
The displacement versus time graph for a body moving in a straight line in shown in figure. Which of the following regions represents the motion when no force is acting on the body
A.
ab
B.
bc
C.
cd
D.
de
IIT-JEE 1970 Basic Level Q116 Errorless Velocity Time Graph MCQ
A lift is going up. The variation in the speed of the lift is as given in the graph. What is height to which the lift takes the passenger
A.
3.6 m
B.
28.8 m
C.
36.0 m
D.
Cannot be calculated from the above graph
Q117 Allen JEE-Main Pattern MCQ
Find ratio of average speed and magnitude of average velocity of tip of minute hand in 20 minutes:
A.
$\frac{2\pi}{3\sqrt{3}}$
B.
$\frac{2\pi}{3}$
C.
$\frac{3\sqrt{3}}{2\pi}$
D.
None
Q118 Allen JEE-Main Pattern MCQ
The motion of a particle is defined by the position vector $\vec{r} = A(\cos t + t\sin t)\hat{\imath} +A(\sin t - t\cos t)\hat{j}$ Where t is expressed in seconds. Determine the value of t for which positions vectors and acceleration vector are perpendicular.
A.
0
B.
1
C.
3
D.
5
Q119 Allen JEE-Main Pattern MCQ
Now the particle is moving only along the z-axis, and its position is given by, $(t^{2}-2t-3)\hat{k}$ . At what time does the particle stand still?
A.
1
B.
3
C.
5
D.
7
Q120 Allen JEE-Main Pattern MCQ
A particle is moving towards East with velocity $8 \, ms^{-1}$ and acceleration $4 \, ms^{-2}$ directed towards West. Find the distance travelled in 6 seconds.
A.
40 m
B.
24 m
C.
32 m
D.
16 m
Q121 Allen JEE-Main Pattern MCQ
A car moving at 160 km/h when crosses the marker-0, driver applies brake and reduces its speed uniformly to 40 km/h at marker-2. The markers are spaced at equal distances along the road as shown below. At which part of the track would the car have been traveling at instantaneous speed of 100 km/h?
A.
At marker-1
B.
Between marker-0 and marker-1
C.
Between marker-1 and marker-2
D.
More information required to decide.
Q122 Allen JEE-Main Pattern MCQ
Two balls are projected simultaneously from the top of a tall building, one vertically upward and other vertical downwards with the same speed of 60 m/s. Then time interval between the balls striking the ground is :-
A.
6 sec.
B.
10 sec.
C.
12 sec.
D.
9 sec.
Q123 Allen JEE-Main Pattern MCQ
A particle moves on x-axis as per equation $x = (t^{3} - 9t^{2} + 15t + 2)m$ . Distance travelled by the particle between t = 0 and t = 5 s is
A.
25 m
B.
39 m
C.
23 m
D.
52 m
Q124 Allen JEE-Main Pattern MCQ
The $\mathrm{XI^{th}}$ class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At $t = 0$ , the rocket is at $y = 0$ with $V_{y}(t = 0) = 0$ . The velocity of the rocket is given by: $V_{y} = (24t - 3t^{2})m / s$ for $0 \leq t \leq t_{b}$ where $t_{b}$ is the time at which fuel burns out. Vertically upward direction is taken as positive. $(g = 10m / s^2)$ The time taken by rocket to reach its maximum height is
A.
4 sec.
B.
8 sec.
C.
8.8 sec.
D.
9.6 sec.
Q125 Allen JEE-Main Pattern MCQ
Acceleration-velocity graph of a moving particle is shown in figure. The particle is
A.
speeding up at P
B.
speeding up at Q
C.
speeding up at S
D.
speeding down at R