BM Sharma Solutions for Chapter: Basic Mathematics, Exercise 2: DPP

For a particle moving along a straight line with constant acceleration $\left(a\right)$, we define velocity of the particle with time as, $v=u+at$ ($u=$ initial velocity).

Draw the velocity-time graph of the particle in following situations.

$\left(\mathrm{i}\right)$ Velocity is decreasing with time (i.e., acceleration in negative).

$\left(\mathrm{ii}\right)$ Initial velocity is negative, but the acceleration is positive.

A particle is moving along the $x-$direction with a constant acceleration $a$. The particle starts from $x=x_0$ position with an initial velocity $u$. We can define the position of the particle with time by the relation,

$x=x_{\mathit{0}}+ut+\frac{1}{2}a{t}^{\mathit{2}}$

Plot the position of the particle in relation to time in the following situation.

$\left(\mathrm{i}\right)$ If the initial position of the particle is on the negative axis of distance, the initial velocity is positive and acceleration is negative.

$\left(\mathrm{ii}\right)$ If the initial position is positive, the initial velocity is negative and acceleration is positive.

A body is attached to a spring whose other end is fixed. If the spring is elongated by $x$, its potential energy is $U=5x^2$, where, $x$ is in meter and $U$ is in Joule. $U-x$ graph is

A particle starts moving with a constant velocity $v=2 \mathrm{m} {\mathrm{s}}^{-1}$ from the position $x=5 \mathrm{m}$. The position-time graph will be

A stone is allowed to fall freely from a certain height. Neglecting the air resistance, which graph represents the variation of velocity $v$ with time $t$?

Relation between $x$ and $y$ is given by, $y=x^2+2x-3$, then graph of $y=f\left(x\right)$ is:

The velocity displacement graph of a particle moving along a straight line is shown in the figure.

The velocity as a function of $x\left(0\le x\le 1\right)$ is

Which of the following best represents the graph of velocity $\left(v\right)$ versus displacement $\left(s\right)$, for a particle travelling with an acceleration (uniform) and some non-zero initial velocity?