A man can swim certain distance in still water up and down in time $t_1$. If he swims to some distance down stream the river and returns back to same point he takes time $t_2$. Then,

A train of length $210 \mathrm{m}$ is moving with a speed of $25 \mathrm{m} {\mathrm{s}}^{-1}$ in North direction. A small bird is flying above the train with a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ in south direction. Find the time taken by the bird to cross the train in seconds.

A boy standing on the foothpath tosses a ball straight up and catches it. The driver of a car passing by moving with uniform velocity sees this.

The trajectory of the ball as seen by the driver will be

A particle of unit mass undergoes one dimensional motion such that its velocity varies according to $\mathrm{v}\left(\mathrm{x}\right)={\mathrm{bx}}^{-2\mathrm{n}}$, where b and n are constants and $\mathrm{x}$ is the position of the particle. The acceleration of the particle as the function of $\mathrm{x}$, is given by: