# Two cars A and B are travelling in the same direction with velocities v1 and v2 $\left({v}_{1}>{v}_{2}\right)$. When the car A is at a distance d behind car B, the driver of the car A applied the brake producing uniform retardation a. There will be no collision when- 1. $d<\frac{{\left({v}_{1}-{v}_{2}\right)}^{2}}{2a}$ 2. $d<\frac{{v}_{1}^{2}-{v}_{2}^{2}}{2a}$ 3. $d>\frac{{\left({v}_{1}-{v}_{2}\right)}^{2}}{2a}$ 4. $d>\frac{{v}_{1}^{2}-{v}_{2}^{2}}{2a}$

Subtopic:  Relative Motion in One Dimension |
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A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 seconds on it, it moves with a velocity 2 m/sec in the opposite direction. The acceleration produced in it is

(1) 3 m/sec2

(2) –3 m/sec2

(3) 0.3 m/sec2

(4) –0.3 m/sec2

Subtopic:  Acceleration |
77%
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A body starts from rest from the origin with an acceleration of $6\text{\hspace{0.17em}}m/{s}^{2}$ along the x-axis and $8\text{\hspace{0.17em}}m/{s}^{2}$ along the y-axis. Its distance from the origin after 4 seconds will be

(1) 56 m

(2) 64 m

(3) 80 m

(4) 128 m

Subtopic:  Uniformly Accelerated Motion |
75%
From NCERT
PMT - 1999
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A car moving with a velocity of 10 m/s can be stopped by the application of a constant force F in a distance of 20 m. If the velocity of the car is 30 m/s, it can be stopped by this force in

(1) $\frac{20}{3}m$

(2) 20 m

(3) 60 m

(4) 180 m

Subtopic:  Uniformly Accelerated Motion |
72%
From NCERT
PMT - 1999
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The displacement of a particle is given by $$y = a + bt + ct^{2} - dt^{4}$$. The initial velocity and acceleration are, respectively:

 1 $$b, -4d$$ 2 $$-b,2c$$ 3 $$b, ~2c$$ 4 $$2c, -2d$$
Subtopic:  Non Uniform Acceleration |
81%
From NCERT
PMT - 1999
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A car moving with a speed of 40 km/h can be stopped by applying brakes for atleast 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance ?

(1) 8 m

(2) 2 m

(3) 4 m

(4) 6 m

Subtopic:  Uniformly Accelerated Motion |
76%
From NCERT
PMT - 1998
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An elevator car, whose floor to ceiling distance is equal to $$2.7~\text{m}$$, starts ascending with constant acceleration of $$1.2~\text{ms}^{-2}$$. $$2$$ sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is:
1. $$\sqrt{0.54}~\text{s}$$
2. $$\sqrt{6}~\text{s}$$
3. $$0.7~\text{s}$$
4. $$1~\text{s}$$

Subtopic:  Relative Motion in One Dimension |
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The displacement is given by $x=2{t}^{2}+t+5$, the acceleration at $t=2s$ is

(1) $4\text{\hspace{0.17em}\hspace{0.17em}}m/{s}^{2}$

(2) $8\text{\hspace{0.17em}\hspace{0.17em}}m/{s}^{2}$

(3) $10\text{\hspace{0.17em}\hspace{0.17em}}m/{s}^{2}$

(4) $15\text{\hspace{0.17em}\hspace{0.17em}}m/{s}^{2}$

Subtopic:  Uniformly Accelerated Motion |
85%
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Two trains travelling on the same track are approaching each other with equal speeds of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2.0 km apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be

1. 11.8 m/s2

2. 11.0 m/s2

3. 1.6 m/s2

4. 0.8 m/s2

Subtopic:  Uniformly Accelerated Motion |
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A body moves from rest with a constant acceleration of 5 m/s2. Its instantaneous speed (in m/s) at the end of 10 sec is

(1) 50

(2) 5

(3) 2

(4) 0.5

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
86%
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