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.

A body starts falling from height 'h' and if it travels a distance of 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. $\sqrt{3}$ $$ $+$ $2$

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

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: 

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

1. $\frac{1}{2}$

2. $\frac{3}{4}$

3. $\frac{4}{3}$

4. $\frac{3}{2}$

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. $\frac{1}{2}{\mathrm{gt}}^2$

3. $\mathrm{ut}-\frac{1}{2}{\mathrm{gt}}^2$

4. $(\mathrm{u}+\mathrm{gt})\mathrm{t}$

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

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

The position of an object moving along \(\mathrm{x}\)-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

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. \(0\) 

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: