The instantaneous speed is always:

1.	less than the magnitude of instantaneous velocity.
2.	greater than the magnitude of instantaneous velocity.
3.	equal to the magnitude of instantaneous velocity.
4.	may be less or greater than the magnitude of instantaneous velocity.

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 \((\mathrm{x-t})\) 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 \(1,\) \(2\) & \(3,\) 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 $49$ $m$ $s^{-1}.$  How much time does the ball take to return to his hands? 
1. 5 s
2. 10 s
3. 15 s
4. 7 s

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 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. The average speed of the taxi is:
1. 30 km/h
2. 49.3 km/h
3. 55.6 km/h
4. 60 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 car moves with a speed of \(60\) km/h for \(1\) hour in the east direction and with the same speed for \(30\) min in the south direction. The displacement of the car from the initial position is:
1. \(60\) km
2. \(30 \sqrt{2}\)  km
3. \(30 \sqrt{5}\) km
4. \(60 \sqrt{2}\) km

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) $v=\sqrt{\frac{3v_2}{2v_1}}$