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Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q576 Allen PYQ MCQ
A person travelling in a straight line moves with a constant velocity $v_{1}$ for certain distance 'x' and with a constant velocity $v_{2}$ for next equal distance. The average velocity v is given by the relation
A.
$\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
B.
$\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
C.
$\frac{v}{2} = \frac{v_{1} + v_{2}}{2}$
D.
$v = \sqrt{v_{1}v_{2}}$
Q577 Allen PYQ MCQ
A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: $(g = 10 \, \text{m/s}^2)$
A.
300 m
B.
360 m
C.
340 m
D.
320 m
Q578 Allen PYQ MCQ
A person sitting in the ground floor of a building notices through the window, of height 1.5 m, a ball dropped from the roof of the building crosses the window in 0.1 s. What is the velocity of the ball when it is at the topmost point of the window? $(g = 10 \, \text{m/s}^2)$
A.
15.5 m/s
B.
14.5 m/s
C.
4.5 m/s
D.
20 m/s
Q579 Allen PYQ MCQ
A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let $S_{n}$ be the distance travelled by the block in the interval t = n - 1 to t = n. Then, the ratio $\frac{S_{n}}{S_{n+1}}$ is:
A.
$\frac{2n-1}{2n}$
B.
$\frac{2n-1}{2n+1}$
C.
$\frac{2n+1}{2n-1}$
D.
$\frac{2n}{2n-1}$
Q580 Allen PYQ MCQ
A car starts from rest and accelerates at $5 \, m/s^{2}$ . At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t = 6 \, s$ ? (Take $g = 10 \, m/s^{2}$ )
A.
$20 \, m/s, 5 \, m/s^{2}$
B.
$20 \, m/s, 0$
C.
$20\sqrt{2} \, m/s, 0$
D.
$20\sqrt{2} \, m/s, 10 \, m/s^{2}$
Q581 Allen PYQ MCQ
A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle 'Īø' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, Īø, is then given by:
A.
$\theta = \cos^{-1}\left(\frac{gT^{2}}{\pi^{2}R}\right)^{\frac{1}{2}}$
B.
$\theta = \cos^{-1}\left(\frac{\pi^{2}R}{gT^{2}}\right)^{\frac{1}{2}}$
C.
$\theta = \sin^{-1}\left(\frac{\pi^{2}R}{gT^{2}}\right)^{\frac{1}{2}}$
D.
$\theta = \sin^{-1}\left(\frac{2gT^{2}}{\pi^{2}R}\right)^{\frac{1}{2}}$
Q582 Allen PYQ MCQ
The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the x-axis as shown in the figure. The ratio of their respective velocity is :
A.
$1:1$
B.
$1:2$
C.
$1:\sqrt{3}$ $
D.
\sqrt{3}:1$
Q583 Allen PYQ MCQ
The ratio of the distances travelled by a freely falling body in the $1^{st}$ , $2^{nd}$ , $3^{rd}$ and $4^{th}$ second:
A.
1:4:9:16
B.
1:3:5:7
C.
1:1:1:1
D.
1:2:3:4
Q584 Allen PYQ MCQ
A ball is projected with a velocity, $10 \, ms^{-1}$ , at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be:
A.
$5\sqrt{3}ms^{-1}$
B.
$5 \, ms^{-1}$
C.
$10 \, ms^{-1}$
D.
Zero
Q585 Allen PYQ MCQ
A cricket ball is thrown by a player at a speed of 20 m/s in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is: $(g = 10 \, \text{m/s}^{2})$
A.
5 m
B.
10 m
C.
20 m
D.
25 m
Q586 Allen PYQ MCQ
The position-time $(x - t)$ graph for positive acceleration is :
A.
B.
C.
D.
Q587 Allen PYQ MCQ
A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is:
A.
$\frac{2v}{3}$
B.
$\frac{4v}{3}$
C.
$\frac{3v}{4}$
D.
$\frac{v}{3}$
Q588 Allen PYQ MCQ
A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $4 \, ms^{-1}$ . The ball strikes the water surface after 4s. The height of bridge above water surface is (Take g = $10 \, m \, s^{-2}$ )
A.
60 m
B.
64 m
C.
68 m
D.
56 m
Q589 Allen PYQ MCQ
A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$ . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
A.
24 cm
B.
28 cm
C.
30 cm
D.
27 cm
Q590 Allen PYQ MCQ
The position of a particle is given by $\vec{r}(t) = 4t\hat{i} + 2t^2\hat{j} + 5\hat{k}$ where t is in seconds and r in metre. Find the magnitude and direction of velocity v(t), at t = 1s, with respect to x-axis
A.
$4\sqrt{2} \text{ ms}^{-1}$ , $45^\circ$
B.
$4\sqrt{2} \text{ ms}^{-1}$ , $60^\circ$
C.
$3\sqrt{2} \text{ ms}^{-1}$ , $30^\circ$
D.
$3\sqrt{2} \text{ ms}^{-1}$ , $45^\circ$
Q591 Allen PYQ MCQ
A ball is projected from point A with velocity $20 \, m s^{-1}$ at an angle $60^{\circ}$ to the horizontal direction. At the highest point B of the path (as shown in figure), the velocity $v \, m s^{-1}$ of the ball will be:
A.
20
B.
$10\sqrt{3}$
C.
Zero
D.
10
Q592 Allen PYQ MCQ
The velocity (v) - time (t) plot of the motion of a body is shown below: The acceleration $(a)$ - time $(t)$ graph that best suits this motion is:
A.
B.
C.
D.
Q593 Allen PYQ MCQ
A particle is moving along x-axis with its position (x) varying with time (t) as $x = \alpha t^{4} + \beta t^{2} + \gamma t + \delta$ . The ratio of its initial velocity to its initial acceleration, respectively is:
A.
$2\alpha:\delta$
B.
$\gamma:2\delta$
C.
$4\alpha:\beta$
D.
$\gamma:2\beta$
Q594 Allen ANALYTICAL QUESTIONS MCQ
For ground to ground projectile motion with initial velocity u at angle $\theta$ from horizontal. Match Column-I with Column-II
Column-IColumn-II
(P)Change in speed from initial to final point
(Q)Magnitude of change in velocity from initial to final point
(R)Change in speed from initial to top
(S)Magnitude of change in velocity from initial to top
(I)$u-u\cos\theta$
(II)$u\sin\theta$
(III)$2u\sin\theta$
(IV)zero
A.
P-I, Q-II, R-III, S-IV
B.
P-IV, Q-II, R-I, S-III
C.
P-IV, Q-III, R-I, S-II
D.
P-IV, Q-III, R-II, S-I
Q595 Allen ANALYTICAL QUESTIONS MCQ
For initial velocity $(\vec{v}_{i})=3\hat{i}-4\hat{j}$ and final velocity $(\vec{v}_{f})=3\hat{i}+4\hat{j}$ :Match Column-I with Column-II
Column-IColumn-II
(P)$|\Delta \vec{v}|$
(Q)$\Delta |\vec{v}|$
(R)$\vec{v}_f-\vec{v}_i$
(S)$\vec{v}_f+\vec{v}_i$
(I)$8\hat{j}$
(II)$6\hat{i}$
(III)$0$
(IV)$8$
A.
P-III, Q-IV, R-II, S-I
B.
P-III, Q-IV, R-I, S-II
C.
P-IV, Q-III, R-II, S-I
D.
P-IV, Q-III, R-I, S-II
Q596 Allen ANALYTICAL QUESTIONS MCQ
A particle is projected vertically upward from ground with initial velocity u such that it clears the top of a pole of height h after time $t_{1}$ in its path. It takes further time $t_{2}$ to reach the ground. Match Column-I with Column-II
Column-IColumn-II
(P)$u$
(Q)$h$
(R)Time of flight
(S)Maximum height
(I)$\dfrac{(t_1+t_2)^2}{8}g$
(II)$(t_1+t_2)$
(III)$\dfrac{1}{2}g(t_1+t_2)$
(IV)$\dfrac{1}{2}gt_1t_2$
A.
P-II, Q-I, R-III, S-IV
B.
P-I, Q-II, R-III, S-IV
C.
P-III,Q-IV, R-II, S-I
D.
P-IV, Q-II, R-II, S-I
Q597 Allen ANALYTICAL QUESTIONS MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Horizontal component of velocity is constant in projectile motion under gravity.
Reason (R) : Two projectiles having same horizontal range must have the same time of flight.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
(A) is false but (R) is true.
Q598 Allen ANALYTICAL QUESTIONS MCQ
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A particle with constant acceleration always moves along a straight line.
Reason (R): A particle with constant acceleration will not change direction of motion.
In the light of the above statements,
choose the most appropriate answer from the options given below:
A.
Both (A) and (R) are true and (R) is the correct explanation of (A).
B.
Both (A) and (R) are true and (R) is NOT the correct explanation of (A).
C.
(A) is true but (R) is false.
D.
Both (A) and (R) are false.
Q599 Allen ANALYTICAL QUESTIONS MCQ
An object may have-
(A) varying speed without having varying velocity
(B) varying velocity without having varying speed
(C) non-zero acceleration without having varying velocity
(D) non-zero acceleration without having varying speed
A.
Only B is correct
B.
Only D is correct
C.
Both B and D are correct
D.
All are correct
Q600 Allen ANALYTICAL QUESTIONS MCQ
The velocity of a particle is zero at t = 0, then -

(A) the acceleration at t = 0 must be zero

(B) the acceleration at t = 0 may be zero

(C) if the acceleration is zero from t = 0 to t = 10 s, speed is also zero in this interval

(D) if the speed is zero from t = 0 to t = 10 sec, the acceleration is also zero in the interval

A.
(A), (C) and (D) are correct
B.
(B), (C) and (D) are correct
C.
(A) and (D) are correct
D.
(B) and (C) are correct