Exercise

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3} \mathrm{m} {\mathrm{s}}^{-2}$ in $3^{rd}$ second is

A car moving on a straight road covers one third of the distance with $20 \mathrm{km} {\mathrm{h}}^{-1}$ and the rest with $60 \mathrm{km} {\mathrm{h}}^{-1}$. The average speed of the car is,

A particle is moving such that its position coordinates$(x,y)$ are $(2m,3m)$ at time $t=0$, $(6m,7m)$ at time $t=2 s$ and $(13 m, 14 m)$ at time $t=5 s$. Average velocity vector $\left(\overrightarrow{v_{av}}\right)$ from $t=0$ to $t=5 s$ is:

A balloon is ascending at the rate of $14 {\mathrm{ms}}^{-1}$at a height of $98 \mathrm{m}$ above the ground when a packet is dropped from the balloon. After how much time and with what velocity does it reach the ground?

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10 m{s}^{-1}$ to $20 m{s}^{-1}$ while passing through a distance $135 m$ In t second. The value of $t$ is:

A boy sitting on the topmost berth in the compartment of a train which is just going to stop on a railway station drops an apple aiming at the open hand of his brother sitting vertically below his hands at a distance of about $2 \mathrm{m}$. The apple will fall

A passenger train of length $60 \mathrm{m}$ travels at a speed of $80 \mathrm{km} {\mathrm{hr}}^{-1}$. Another freight train of length $120 \mathrm{m}$ travels at a speed of $30 \mathrm{km} {\mathrm{hr}}^{-1}$. The ratio of times taken by the passenger train to completely cross the freight train when : $\left(\mathrm{i}\right)$ they are moving in the same direction and $\left(\mathrm{ii}\right)$ in the opposite direction is

The driver of a train moving at 72 km ${\mathrm{h}}^{-1}$ sights another train moving at 4 $\mathrm{m }{\mathrm{s}}^{-1}$ on the same track and in the same direction. He instantly applies brakes to produce a retardation of 1 $\mathrm{m }{\mathrm{s}}^{-2}$. The minimum distance between the trains so that no collision occurs is