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Kinematics-1D

116 Questions Start Objective Test
All Exams Allen Objective Errorless
Q51 Objective 1. Taking it together MCQ
The velocity v of a particle as a function of its position (x) is expressed as $ v = \sqrt{c_{1} - c_{2}x} $ , where $ c_{1} $ and $ c_{2} $ are positive constants. The acceleration of the particle is
A.
$c_{2}$
B.
$-\frac{c_2}{2}$
C.
$c_{1} - c_{2}$
D.
$\frac{c_1 + c_2}{2}$
Q52 Objective 1. Taking it together MCQ
A person walks up a stalled escalator in 90 s. When he is just standing on the same moving escalator, then he is carried for 60 s. The time it would take him to walk up the moving escalator will be
A.
27 s
B.
50 s
C.
18 s
D.
36 s
Q53 Objective 1. Taking it together MCQ
Particle A is moving along X-axis. At time t = 0, it has velocity of $ 10 \, ms^{-1} $ and acceleration $ -4 \, ms^{-2} $ . Particle B has velocity of $ 20 \, ms^{-1} $ and acceleration $ -2 \, ms^{-2} $ . Initially both the particles are at origin. At time t = 2 s, distance between the two particles is
A.
24 m
B.
36 m
C.
20 m
D.
42 m
Q54 Objective 1. Taking it together MCQ
The displacement of a body along X-axis depends on time as $ \sqrt{x} = t + 1 $ . Then, the velocity of body
A.
increases with time
B.
decreases with time
C.
independent of time
D.
None of these
Q55 Objective 1. Taking it together MCQ
A car starts moving along a line, first with acceleration $ a = 5 \, ms^{-2} $ starting from rest, then uniformly and finally decelerating at the same rate a and comes to rest. The total time of motion is $ 25 \, s $ . The average speed during the time is $ 20 \, ms^{-1} $ . How long does particle move uniformly?
A.
10 s
B.
12 s
C.
20 s
D.
15 s
Q56 Objective 1. Taking it together MCQ
A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along QQ as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is figure
A.
0.1
B.
$\frac{\pi + 4}{2}$, 0
C.
21.4, $\frac{\pi + 4}{2}$
D.
0,214
Q57 Objective 1. Taking it together MCQ
A body starts from rest with uniform acceleration a. The acceleration of the body as function of time t is given by the equation $ a = pt $ , where p is a constant, then the displacement of the particle in the time interval t = 0 to $ t = t_{1} $ will be
A.
$\frac{1}{2} pt_1^2$
B.
$\frac{1}{3} pt_1^2$
C.
$\frac{1}{2} pt_1^2$
D.
$\frac{1}{6} pt_1^3$
Q58 Objective 1. Taking it together MCQ
A particle moves along a straight line OX. At a time t (in seconds), the distance $ x = 40 + 12t - t^{3} $ . How long would the particle travel before coming to rest?
A.
24 m
B.
40 m
C.
56 m
D.
16 m
Q59 Objective 1. 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
Q60 Objective 1. 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
Q61 Objective 1. 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.
$660\mathrm{ms}^{-1}$
Q62 Objective 1. 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.
$4105\mathrm{ms}^{-2}$
Q63 Objective 1. 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.
$a / (v + v_{1})$
Q64 Objective 1. 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
Q65 Objective 1. 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
Q66 Objective 1. 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
Q67 Objective 1. 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
Q68 Objective 1. 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.
$x = \sqrt{t + a}$
Q69 Objective 1. 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.
$25\mathrm{m}$
Q70 Objective 1. 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} $
Q71 Objective 1. 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.
$16\mathrm{ms}^{-2}$
Q72 Objective 1. 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.
$15\mathrm{ms}^{-1}$
Q73 Objective 1. 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.
$16\mathrm{ms}^{-1}$
Q74 Objective 1. 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.
$-1 / x^{3}$
Q75 Objective 1. 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.
$(v_{1} - v_{2}):(v_{2} - v_{3}) = (t_{1} - t_{2}):t_{2} - t_{3})$