BM Sharma Solutions for Chapter: Motion in One Dimension, Exercise 1: DPP

A man walks on a straight road from his home to a market $2.5 \mathrm{km}$ away with a speed of $5 \mathrm{km} {\mathrm{h}}^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5 \mathrm{km} {\mathrm{h}}^{-1}$. The average speed of the man over the interval of time $0$ to $40 \min$ is equal to

Consider the acceleration, velocity and displacement of a tennis ball as it falls to the ground and bounces back. Direction of which of these changes in the process?

The position of a particle moving in the $xy$ - plane at any time $t$ is given by $x=(3t^2-6t) \mathrm{metre}$, and $y=(t^2-2t) \mathrm{metre}$. Select the correct statement about the moving particle from the following.

The acceleration $a$ $\mathrm{m} {\mathrm{s}}^{-2}$ of a particle is given by $a=3t^2+2t+2$, where $t$ is the time. If the particle starts out with a velocity $u=2 \mathrm{m} {\mathrm{s}}^{-1}$, at $t=0$, then, the velocity at the end of $2$ $\mathrm{s}$ is

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x=7t+4t^2$ and $y= 5t$, where $x$ and $y$ are in $\mathrm{meter}$ and $t$ is in $\mathrm{second}$. The acceleration of particle at $t=5 \mathrm{s}$ is

Which of the following statements are correct?

A particle is moving on the $x-$ axis. If initial velocity $u>0$, and acceleration $a<0$, and $a$ is constant, then the number of possible values of the time for which the particle is at distance $d$ from its starting point may be

For a particle moving in a straight line with increasing speed, the appropriate sign of acceleration $\overrightarrow{\mathit{a}}$ and velocity $\overrightarrow{\mathit{v}}$ can be: