If the velocity of a body related to displacement ${x}$ is given by $v=\sqrt{5000+24 {x}} \;{m} / {s}$, then the acceleration of the body is $\ldots \ldots {m} / {s}^{2}$

A particle starts moving from rest in a straight line with constant acceleration. After time $t_0$, acceleration changes its sign (just opposite to the initial direction), remaining the same in magnitude. Determine the time from the beginning of motion in which the particle returns to the initial position.

Which of the following represents uniformly accelerated motion?

An object at rest at the origin begins to move in the $+x$-direction with a uniform acceleration of $1 \,m / s ^2$ for $4 \,s$ and then it continues moving with a uniform velocity of $4 \,m / s$ in the same direction.The $x-t$ graph for object's motion will be

A smooth inclined plane is inclined at an angle $\theta$ with horizontal. A body starts from rest and slides down the inclined surface. Then the time taken by it to reach the bottom is