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 |
82%
From NCERT
PMT - 1999
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The position $$x$$ of a particle varies with time $$t$$ as $$x=at^2-bt^3$$. The acceleration of the particle will be zero at time $$t$$ equal to:

 1 $$\dfrac{a}{b}$$ 2 $$\dfrac{2a}{3b}$$ 3 $$\dfrac{a}{3b}$$ 4 zero

Subtopic:  Acceleration |
85%
From NCERT
PMT - 1997
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A student is standing at a distance of $$50$$ metres from the bus. As soon as the bus begins its motion with an acceleration of $$1$$ ms–2, the student starts running towards the bus with a uniform velocity $$u$$. Assuming the motion to be along a straight road, the minimum value of $$u$$, so that the student is able to catch the bus is:
1. $$5$$ ms–1
2. $$8$$ ms–1
3. $$10$$ ms–1
4. $$12$$ ms–1

Subtopic:  Uniformly Accelerated Motion |
73%
From NCERT
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A body starts to fall freely under gravity. The distances covered by it in the first, second and third second will be in the ratio:
1. $$1:3:5$$
2. $$1:2:3$$
3. $$1:4:9$$
4. $$1:5:6$$

Subtopic:  Uniformly Accelerated Motion |
87%
From NCERT
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A particle moving in a straight line covers half the distance with a speed of $$3~\text{m/s}$$. The other half of the distance is covered in two equal time intervals with speeds of $$4.5~\text{m/s}$$ and $$7.5~\text{m/s}$$ respectively. The average speed of the particle during this motion is:
1. $$4.0~\text{m/s}$$
2. $$5.0~\text{m/s}$$
3. $$5.5~\text{m/s}$$
4. $$4.8~\text{m/s}$$

Subtopic:  Average Speed & Average Velocity |
70%
From NCERT
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A stone dropped from a building of height $$h$$ and reaches the earth after $$t$$ seconds. From the same building, if two stones are thrown (one upwards and other downwards) with the same velocity $$u$$ and they reach the earth surface after $$t_1$$ and $$t_2$$ seconds respectively, then:

1. $t={t}_{1}-{t}_{2}$

2. $t=\frac{{t}_{1}+{t}_{2}}{2}$

3. $t=\sqrt{{t}_{1}{t}_{2}}$

4. $t={t}_{1}^{2}{t}_{2}^{2}$

Subtopic:  Uniformly Accelerated Motion |
77%
From NCERT
PMT - 1997
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The velocity-time $$(v\text-t)$$ graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $$6$$ s are, respectively:

1. $$8$$ m, $$16$$ m
2. $$16$$ m, $$8$$ m
3. $$16$$ m, $$16$$ m
4. $$8$$ m, $$8$$ m

Subtopic:  Graphs |
78%
From NCERT
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In the following graph, the distance travelled by the body in metres is:

 1 $$200$$ 2 $$250$$ 3 $$300$$ 4 $$400$$
Subtopic:  Graphs |
86%
From NCERT
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Given below are two statements:

 Assertion (A): Position-time graph of a stationary object is a straight line parallel to the time axis. Reason (R): For a stationary object, the position does not change with time.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 Both (A) and (R) are False.
Subtopic:  Distance & Displacement |
88%
From NCERT
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The acceleration of a particle starting from rest varies with time according to the relation $$A= - a\omega^2\sin \omega t$$. The displacement of this particle at a time $$t$$ will be:
1. $$-\frac{1}{2}\left(a\omega^2\sin\omega t\right)t^2$$
2. $$a\omega \sin \omega t$$
3. $$a\omega \cos \omega t$$
4. $$a\sin \omega t$$​​​​​​​

Subtopic:  Non Uniform Acceleration |
60%
From NCERT
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