# 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 |
From NCERT
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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%
From NCERT
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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 |
From NCERT
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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%
From NCERT
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A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. The distance covered by the boggy and distance covered by the train in the same time has relation

(1) Both will be equal

(2) First will be half of second

(3) First will be 1/4 of second

(4) No definite ratio

Subtopic:  Uniformly Accelerated Motion |
From NCERT
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A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 3rd second

(1) $\frac{7}{5}$

(2) $\frac{5}{7}$

(3) $\frac{7}{3}$

(4) $\frac{3}{7}$

Subtopic:  Uniformly Accelerated Motion |
86%
PMT - 1993
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The acceleration $$a$$ in m/s2 of a particle is given by $a=3{t}^{2}+2t+2$ where t is the time. If the particle starts out with a velocity, $$u=2$$ m/s at t = 0, then the velocity at the end of $$2$$ seconds will be:
1. $$12$$ m/s
2. $$18$$ m/s
3. $$27$$ m/s
4. $$36$$ m/s

Subtopic:  Acceleration |
73%
From NCERT
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A particle moves along a straight line such that its displacement at any time $$t$$ is given by $$S = t^{3} - 6 t^{2} + 3 t + 4$$ metres. The velocity when the acceleration is zero is:

 1 $$4$$ ms-1 2 $$-12$$ ms−1 3 $$42$$ ms−1 4 $$-9$$ ms−1
Subtopic:  Acceleration |
81%
From NCERT
PMT - 1994
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