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 $.........m/s^2$

Starting from rest, acceleration of a particle is $a = 2(t - 1).$ The velocity of the particle at $t = 5\,s$ is.........$m/sec$

The velocity of a bullet is reduced from $200\,m/s$ to $100\,m/s $ while travelling through a wooden block of thickness $10\,cm$. The retardation, assuming it to be uniform, will be 

A train accelerates from rest at a constant rate $\alpha$ for distance $x_1$ and time $t_1$. After that it retards to rest at constant rate $\beta$ for distance $x_2$ and time $t_2$. Which of the following relations is correct?

The velocity-time graphs of a car and a scooter are shown in the figure. $(i)$ the difference between the distance travelled by the car and the scooter in $15\, s$ and $(ii)$ the time at which the car will catch up with the scooter are, respectively

Acceleration versus time graph of a body starting from rest is shown in the figure. The velocity versus time graph of the body is given by