The velocity of a particle moving in the positive direction of $x$-axis varies as $v=5 \sqrt{x}$. Assuming that at $t=0$, particle was at $x=0$. What is the acceleration of the particle $.........m/s^2$

Velocity of a body moving along a straight line with uniform acceleration $a$ reduces by $\frac{3}{4}$ of its initial velocity in time $t_0$. The total time of motion of the body till its velocity becomes zero is

A train moves from rest with a uniform acceleration $a$ . Attaining a maximum speed $v$ it  starts moving with uniform retardation $a$ . Assuming $s$ = total distance covered in the  unidirectional motion of the train, its total time of journey and maximum speed are  (respectively).

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s) - $ velocity $(v)$ graph of this object is

The same retarding force is applied to stop a train. The train stops after $80\, m$. If the speed is doubled, then the stopping distance will be