Chittaranjan Dasgupta and Asok Kumar Das Solutions for Chapter: Motion of a Particle, Exercise 1: EXERCISE

A car on applying brake, stops after $5$ seconds covering $25 \mathrm{m}$ with uniform retarded motion. The initial speed of the car is

A car travelling on a straight road moves with a uniform velocity ${\nu }_1$ for some time and with uniform velocity ${\nu }_2$ for the next equal time. The average velocity of the car is

A ball is projected horizontally with a velocity of $5 \mathrm{m}/\mathrm{s}$ from the top of a building $19.6 \mathrm{m}$ high. How long will the ball take to hit the ground ?

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in air for (Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

If a person can throw a stone vertically up to a maximum height of $\mathrm{h}$ metre, then the maximum distance through which he can throw it in the horizontal direction is

A particle moving with uniform acceleration moves $24 \mathrm{m}$ and $64 \mathrm{m}$ in two consecutive $4 \mathrm{s}$ interval. The initial velocity of the particle is

The acceleration in ${\mathrm{ms}}^{-2}$ of a particle is given by a $a=3t^2+2t+2$. At $t=0$, the particle starts with a velocity $2 {\mathrm{ms}}^{-1}$. After $2 \mathrm{s}$, the velocity will be

The displacement of a particle moving in a straight line is given by $\mathrm{S}=\left({\mathrm{t}}^3-6{\mathrm{t}}^2+3\mathrm{t}+4\right) \mathrm{m}$. When there is no acceleration, the velocity is