An object,moving with a speed of $6.25 \ m/s$,is decelerated at a rate given by: $\frac{dv}{dt} = - 2.5\sqrt{v}$,where $v$ is the instantaneous speed. The time taken by the object to come to rest would be ........ $s$.

An object accelerates from rest to a velocity $27.5 \,m/s$ in $10 \,s$. Find the distance covered by the object in the next $10 \,s$ (in $m$).

The displacement of a particle moving with uniform acceleration in time $t$ is given by $S = 30t + 5t^2$. Its initial velocity is $.......$ (in $m \ s^{-1}$)

The displacement of a particle after time $t$ is given by $x = (k/b^2)(1 - e^{-bt})$ where $b$ is a constant. What is the acceleration of the particle?

The speeds of two identical cars are $u$ and $4u$ at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is

If the engine of a long train moving with constant acceleration crosses a tree with velocity $u$ and the last compartment of the train crosses the same tree with velocity $v$,then the velocity with which the middle compartment crosses the same tree is