If a body travels some distance in a given time interval, then for that time interval, its: 1. Average speed  ≥  |Average velocity| 2. |Average velocity|  ≥  Average speed 3. Average speed < |Average velocity| 4. |Average velocity| must be equal to average speed.

Subtopic:  Average Speed & Average Velocity |
84%
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A body starts falling from height $$h$$ and if it travels a distance of $$\frac{h}{2}$$ during the last second of motion, then the time of flight is (in seconds):
1. $$\sqrt{2}-1$$
2. $$2+\sqrt{2}$$
3. $$\sqrt{2}+\sqrt{3}$$
4. $$\sqrt{3}+2$$

Subtopic:  Uniformly Accelerated Motion |
From NCERT
AIPMT - 1999
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For a particle, displacement time relation is given by $t$ $=$ $\sqrt{x}$ $+$ $3$ . Its displacement, when its velocity is zero will be:
1. $$2$$ m
2. $$4$$ m
3. $$0$$
4. none of the above

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
81%
From NCERT
AIPMT - 1999
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A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time-average velocity is:
where time-average velocity and space-average velocity, respectively, are defined as follows:

$}_{time}$ $=$ $\frac{\int vdt}{\int dt}$
$}_{space}$ $=$ $\frac{\int vds}{\int ds}$

 1 $$\frac{1}{2}$$ 2 $$\frac{3}{4}$$ 3 $$\frac{4}{3}$$ 4 $$\frac{3}{2}$$
Subtopic:  Average Speed & Average Velocity |
From NCERT
AIPMT - 1999
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If a ball is thrown vertically upwards with speed $$u$$, the distance covered during the last $$t$$ seconds of its ascent is:
1. $$ut$$
2. $$\frac{1}{2}gt^2$$
3. $$ut-\frac{1}{2}gt^2$$
4. $$(u+gt)t$$

Subtopic:  Uniformly Accelerated Motion |
65%
From NCERT
AIPMT - 2003
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A man throws some balls with the same speed vertically upwards one after the other at an interval of $$2$$ seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given $$g = 9.8$$ m/s2)

 1 More than $$19.6$$ m/s 2 At least $$9.8$$ m/s 3 Any speed less than $$19.6$$ m/s 4 Only with a speed of $$19.6$$ m/s
Subtopic:  Uniformly Accelerated Motion |
66%
From NCERT
AIPMT - 2003
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A car is moving along a straight line, say OP in the figure. It moves from O to P in $$18$$ s and returns from P to Q in $$6.0$$ s. The average velocity and average speed of the car in going from O to P and back to Q respectively are:

1. $$10$$ m/s & $$10$$ m/s

2. $$20$$ m/s & $$30$$ m/s

3. $$20$$ m/s & $$20$$ m/s

4. $$10$$ m/s & $$20$$ m/s

Subtopic:  Average Speed & Average Velocity |
70%
From NCERT
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The position of an object moving along $$x$$-axis is given by $$x=a+bt^2$$, where $$a=8.5$$ m, $$b=2.5$$ ${\mathrm{ms}}^{-2}$ and $$t$$ is measured in seconds. Its average velocity between $$t=2.0$$ s and $$t=4.0$$ s is:
1. $$10$$ m/s
2. $$15$$ m/s
3. $$20$$ m/s
4. $$25$$ m/s

Subtopic:  Average Speed & Average Velocity |
64%
From NCERT
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The position of an object moving along the x-axis is given by, $$x=a+bt^2$$  where $$a=8.5$$ m,
$$b=2.5$$ ms-2
and $$t$$ is measured in seconds. Its velocity at $$t=2.0$$ s will be:
1. $$13$$ m/s
2. $$17$$ m/s
3. $$10$$ m/s
4. $$0$$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
86%
From NCERT
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The displacement $$x$$ of a particle varies with time $$t$$ as $$x = ae^{-\alpha t}+ be^{\beta t}$$$\mathrm{}$
, where $$a,$$ $$b,$$ $$\alpha,$$ and $$\beta$$ are positive constants. The velocity of the particle will:

 1 be independent of $$\alpha$$ and $$\beta.$$ 2 go on increasing with time. 3 drop to zero when $$\alpha=\beta.$$ 4 go on decreasing with time.
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
52%
From NCERT
AIPMT - 2005
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