For a particle moving along a straight line path, the displacements in the third and fifth seconds of its motion are $10 \ m$ and $18 \ m$ respectively. The speed of the particle at time $t=4 \ s$ is (in $ms^{-1}$)

$A$ rifle bullet loses $1/20^{th}$ of its velocity in passing through a wooden plank. The least number of planks required to stop the bullet is :-

$A$ particle starts from the origin at time $t=0$ and moves in the positive $x$-direction. Its velocity $v$ varies with time as $v=10t \text{ cm/s}$. The distance covered by the particle in $8 \text{ s}$ will be: (in $\text{ cm}$)

The displacement $(x)$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$. Choose the incorrect statements from the following.

The distance travelled by a particle is proportional to the square of time. Then,the particle travels with:

The deceleration experienced by a moving motor boat,after its engine is cut-off,is given by $\frac{dv}{dt} = -kv^3$,where $k$ is a constant. If $v_0$ is the magnitude of the velocity at cut-off,the magnitude of the velocity at a time $t$ after the cut-off is: