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

If v is the velocity of a body moving along x-axis, then acceleration of body is

(1) $\frac{dv}{dx}$

(2) $v\frac{dv}{dx}$

(3) $x\frac{du}{dx}$

(4) $v\frac{dx}{dv}$

If a body is moving with constant speed, then its acceleration

(1) Must be zero

(2) May be variable

(3) May be uniform

(4) Both (2) & (3)

When the velocity of a body is variable, then: