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) $v=\sqrt{\frac{3v_2}{2v_1}}$

The figure shows the graph of the x-coordinate of a particle moving along the x-axis as a function of time. Average velocity during t=0 to 6 s and instantaneous velocity at t=3 s respectively, will be:

1. 10 m/s, 0
2. 60 m/s, 0
3. 0, 0
4. 0, 10 m/s

Position-time graph for a particle is shown in the figure. Starting from t=0, at what time t, the average velocity is zero?

(1) 1 s

(2) 3 s

(3) 6 s

(4) 7 s

A body in one-dimensional motion has zero speed at an instant. At that instant, it must have:

If a particle is moving along a straight line with increasing speed, then:

At any instant, the velocity and acceleration of a particle moving along a straight line are v and a. The speed of the particle is increasing if

(1) v>0, a>0

(2) v<0, a>0

(3) v>0, a<0

(4) v>0, a=0