A man walks on a straight road from his home to a market \(2.5\) km away with a speed of \(5\) km/h. Finding the market closed, he instantly turns and walks back home with a speed of \(7.5\) km/h. What is the magnitude of the average velocity of the man over the interval of time \(0\) to \(30\) min?

1.	\(6\) km/h	2.	\(5\) km/h
3.	\(5.6\) km/h	4.	\(6.6\) km/h

The instantaneous speed is always:

A police van moving on a highway with a speed of $30 km h^{-1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of $192 km h^{-1}$. If the muzzle speed of the bullet is $150 m s^{-1},$ with what speed does the bullet hit the thief’s car? 

$\left(1\right) 103 m s^{-1}$
$\left(2\right) 105 m s^{-1}$
$\left(3\right) 101 m s^{-1}$
$\left(4\right) 102 m s^{-1}$

The figure gives the \((x\text-t)\) plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals \(1,\) \(2\) and \(3,\) respectively are:
                       

The figure gives a speed-time graph of a particle in motion along the same direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude?

A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to \(49~\text{ms}^{-1}.\) How much time does the ball take to return to his hands? 

On a long horizontally moving belt (as shown in the figure) a child runs to and fro with a speed $9 km h^{-1}$ (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of $4 km h^{-1}$. For an observer on a stationary platform outside, what is the speed of the child running in the direction of motion of the belt?

1. 5 kmh^-1
2. \(\sqrt{41}\) kmh^-1
3. 21 kmh^-1
4. 13 kmh^-1

A passenger arriving in a new town wishes to go from the station to a hotel located \(10~\text{km}\) away on a straight road from the station. A dishonest cabman takes him along a circuitous path \(23~\text{km}\) long and reaches the hotel in \(28~\text{min}.\)  The average speed of the taxi is:
1. \(30~\text{km/h}\)
2. \(49.3~\text{km/h}\)
3. \(55.6~\text{km/h}\)
4. \(60~\text{km/h}\)

A particle moves along the x-axis with a speed 6 m/s for the first half distance of a journey second half distance with a speed 3 m/s. The average speed in the total journey is

(1) 5 m/s

(2) 4.5 m/s

(3) 4 m/s

(4) 2 m/s

A person travels along a straight road for the first $\frac{t}{3}$ time with a speed v₁ and for next $\frac{2t}{3}$ time with a speed v₂. Then the mean speed v is given by

(1) $v=\frac{v_1+2v_2}{3}$

(2) $\frac{1}{v}=\frac{1}{3v_1}+\frac{2}{3v_2}$

(3) $v=\frac{1}{3}\sqrt{2v_1{v}_2}$

(4) $v=\sqrt{\frac{3v_2}{2v_1}}$