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:

An object is moving with variable speed, then

(1) Its velocity may be zero

(2) Its velocity must be variable

(3) Its acceleration may be zero

(4) Its velocity must be constant

The position of a particle moving along x-axis is given by $x=10t-2t^2$. Then the time (t) at which it will momently come to rest is

1. 0

2. 2.5 s

3. 5 s

4. 10 s

If the displacement of a particle varies with time as $\sqrt{x}=t+7$, then

(1) Velocity of the particle is inversely proportional to t

(2) Velocity of the particle is proportional to t²

(3) Velocity of the particle is proportional to $\sqrt{t}$

(4) The particle moves with constant acceleration.

The initial velocity of a particle is u (at t=0) and the acceleration a is given by $\alpha t^{3/2}$. Which of the following relations is valid?

(1) $v=u+\alpha t^{3/2}$

(2) $v=u+\frac{3\alpha t^3}{2}$

(3) $v=u+\frac{2}{5}\alpha t^{5/2}$

(4) $v=u+\alpha t^{5/2}$

The position x of a particle moving along the x-axis varies with time t as $x=A \sin \left(\omega t\right)$ where A and $\omega$ are positive constants. The acceleration a of the particle varies with its position (x) as

(1) a = Ax

(2) $a=-{\omega }^{2}x$

(3) $a=A\omega x$

(4) $a={\omega }^2\times A$

A particle moves in a straight line and its position x at time t is given by x² = 2 + t. Its acceleration is given by

(1) $\frac{-2}{x^3}$

(2) $-\frac{1}{2x^2}$

(3) $-\frac{1}{4x^3}$

(4) $\frac{1}{x^2}$