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Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q626 Objective Taking it together MCQ
A bullet emerges from a barrel of length 1.2 m with a speed of $ 640 \, ms^{-1} $ . Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired, is
A.
4 ms
B.
40 ms
C.
$ 400 \mu s $
D.
1 s
Q627 Objective Taking it together MCQ
The ratios of the distance traversed, in successive intervals of time by a body, falling from rest, are
A.
1:3:5:7:9:...
B.
2:4:6:8:10:...
C.
1:4:7:10:13:...
D.
None of these
Q628 Objective Taking it together MCQ
A particle starts from rest. Its acceleration (a) versus time (t) graph as shown in the figure. The maximum speed of the particle will be figure
A.
$110\mathrm{ms}^{-1}$
B.
$55\mathrm{ms}^{-1}$
C.
$550\mathrm{ms}^{-1}$
D.
$660\mathrm{ms}^{-1}$
Q629 Objective Taking it together MCQ
A ball is dropped onto the floor from a height of 10 m. It rebounds to a height of 5 m. If the ball was in contact with the floor for 0.01 s, what was its average acceleration during contact? (Take, $ g = 10 \, ms^{-2} $ )
A.
$2414\mathrm{ms}^{-2}$
B.
$1735\mathrm{ms}^{-2}$
C.
$ 3120 \, ms^{-2} $
D.
$4105\mathrm{ms}^{-2}$
Q630 Objective Taking it together MCQ
Two boys are standing at the ends A and B of a ground, where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity $ v_{1} $ . The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is
A.
$a / \sqrt{v^2 + v_1^2}$
B.
$\sqrt{a^2 / (v^2 - v_1^2)}$
C.
$a / v - v_{1}$
D.
$a / (v + v_{1})$
Q631 Objective Taking it together MCQ
A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. Then, which amongst the following option is correct about the relation between the distance covered by the boggy and distance covered by the train in the same time?
A.
Both will be equal
B.
First will be half of second
C.
First will be 1/4 of second
D.
No definite ratio
Q632 Objective Taking it together MCQ
A body moves for a total of nine second starting from rest with uniform acceleration and then with uniform retardation, which is twice the value of acceleration and then stops. The duration of uniform acceleration is
A.
3 s
B.
4.5 s
C.
5 s
D.
6 s
Q633 Objective Taking it together MCQ
The displacement $ x $ of a particle varies with time $ t $ as $ x = ae^{-at} + be^{\beta t} $, where $ a, b, \alpha $ and $ \beta $ are positive constants. The velocity of the particle will
A.
go on decreasing with time
B.
be independent of $\alpha$ and $\beta$
C.
drop to zero when $\alpha = \beta$
D.
go on increasing with time
Q634 Objective Taking it together MCQ
A stone is allowed to fall freely from rest. The ratio of the time taken to fall through the first metre and the second metre distance is
A.
$\sqrt{2} - 1$
B.
$\sqrt{2} + 1$
C.
$\sqrt{2}$
D.
None of these
Q635 Objective Taking it together MCQ
Amongst the following equation of motion, which represents uniformly accelerated motion?
A.
$x = \sqrt{\frac{t + \alpha}{b}}$
B.
$x = \frac{t + \alpha}{b}$
C.
$t = \sqrt{\frac{x + a}{b}}$
D.
$x = \sqrt{t + a}$
Q636 Objective Taking it together MCQ
A point initially at rest moves along $X$-axis. Its acceleration varies with time as $a = (6t + 5)\mathrm{ms}^{-2}$. If it starts from origin, then the distance covered in 2 s is
A.
$20\mathrm{m}$
B.
$18\mathrm{m}$
C.
$16\mathrm{m}$
D.
$25\mathrm{m}$
Q637 Objective Taking it together MCQ
A particle moves a distance $ x $ in time $ t $ according to equation $ x = (t + 5)^{-1} $. The acceleration of particle is proportional to
A.
(velocity) $ ^{3/2} $
B.
(distance) $ ^{2} $
C.
(distance) $ ^{-2} $
D.
(velocity) $ ^{2/3} $
Q638 Objective Taking it together MCQ
A particle moves along a straight line. Its position at any instant is given by $ x = 32t - \frac{8t^3}{4} $, where $ x $ is in metre and $ t $ is in second. Find the acceleration of the particle at the instant when particle is at rest.
A.
$-16\mathrm{ms}^{-2}$
B.
$-27.6\mathrm{ms}^{-2}$
C.
$32\mathrm{ms}^{-2}$
D.
$16\mathrm{ms}^{-2}$
Q639 Objective Taking it together MCQ
Two particles $ P $ and $ Q $ simultaneously start moving from point $ A $ with velocities $ 15\mathrm{ms}^{-1} $ and $ 20\mathrm{ms}^{-1} $ respectively. The two particles move with accelerations equal in magnitude but opposite in direction. When $ P $ overtakes $ Q $ at $ B $, then its velocity is $ 30\mathrm{ms}^{-1} $. The velocity of $ Q $ at point $ B $ will be
A.
$30\mathrm{ms}^{-1}$
B.
$5\mathrm{ms}^{-1}$
C.
$20\mathrm{ms}^{-1}$
D.
$15\mathrm{ms}^{-1}$
Q640 Objective Taking it together MCQ
A man is 45 m behind the bus when the bus start accelerating from rest with acceleration $ 2.5 \, ms^{-2} $ . With what minimum velocity should the man start running to catch the bus?
A.
$12\mathrm{ms}^{-1}$
B.
$14\mathrm{ms}^{-1}$
C.
$15\mathrm{ms}^{-1}$
D.
$16\mathrm{ms}^{-1}$
Q641 Objective Taking it together MCQ
A point moves in a straight line, so that its displacement $ x $ at time $ t $ is given by $ x^2 = t^2 + 1 $. Its acceleration is
A.
$1 / x$
B.
$1 / x^{3}$
C.
$-1 / x^{2}$
D.
$-1 / x^{3}$
Q642 Objective Taking it together 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.
$(v_{1} - v_{2}):(v_{2} - v_{3}) = (t_{1} - t_{2}):t_{2} - t_{3})$
Q643 Objective Taking it together MCQ
The velocity-time graph for a particle moving along X-axis is shown in the figure. The corresponding displacement-time graph is correctly shown by figure
A.
figure
B.
figure
C.
figure
D.
figure
Q644 Objective Taking it together MCQ
The vertical height of point $ P $ above the ground is twice that of $ Q $. A particle is projected downward with a speed of $ 5\mathrm{ms}^{-1} $ from $ P $ and at the same time, another particle is projected upward with the same speed from $Q$. Both particles reach the ground simultaneously, then
A.
PQ = 30 m
B.
time of flight of stones = 3 s
C.
Both
D.
Both
Q645 Objective Taking it together MCQ
A body falling from a high Minaret travels 40 m in the last 2 seconds of its fall to ground. Height of Minaret in metre is (Take, g = 10 ms $ ^{-2} $ )
A.
60
B.
45
C.
80
D.
50
Q646 Objective Taking it together MCQ
The acceleration-time $(a - t)$ graph for a particle moving along a straight line starting from rest is shown in figure. Which of the following graph is the best representation of variation of its velocity $(v)$ with time $(t)$? figure
A.
figure
B.
figure
C.
figure
D.
figure
Q647 Objective Taking it together MCQ
The given graph shows the variation of velocity with displacement. Which one of the graphs given below correctly represents the variation of acceleration with displacement? figure
A.
a
B.
b
C.
c
D.
d
Q648 Objective Taking it together MCQ
The displacement $ x $ of a particle in a straight line motion is given by $ x = 1 - t - t^2 $. The correct representation of the motion is
A.
figure
B.
figure
C.
figure
D.
figure
Q649 Objective Taking it together MCQ
Among the four graph shown in the figure, there is only one graph for which average velocity over the time interval $ (0, T) $ can vanish for a suitably chosen T. Which one is it? [NCERT Exemplar]
A.
figure
B.
figure
C.
figure
D.
figure
Q650 Objective Taking it together MCQ
A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct? [NCERT Exemplar]
A.
$x < 0, v < 0, a > 0$
B.
$x > 0, v < 0, a < 0$
C.
$x > 0, v < 0, a > 0$
D.
$x > 0, v > 0, a < 0$