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 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:

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

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

If the magnitude of average speed and average velocity over a time interval are the same, then

(1) The particle must move with zero acceleration

(2) The particle must move with non-zero acceleration

(3) The particle must be at rest

(4) The particle must move in a straight line without turning back