Embibe Experts Solutions for Exercise 10: Assignment

A particle moves in a straight line under an acceleration varying linearly with time. Its velocity-time graph is shown in figure. Then

A particle starts from rest at $x=0$ and acceleration varies with $x$ as shown in the figure. Then

Two stones are thrown vertically upwards simultaneously from the same point on the ground with velocities $u_1=40 \mathrm{m} {\mathrm{s}}^{-1}$ $u_2=30 \mathrm{m} {\mathrm{s}}^{-1}$. Which of the following curve(s) represent(s) correct variation with time $t$ ? (Assume that stone does not bounce back after collision with ground)

$\left(y_1-y_2\right)=$ relative separation between stones
$\left(v_1-v_2\right)=$ relative velocity of two stones
$\left(a_1-a_2\right)=$ relative acceleration of two stones

The acceleration of a particle moving in a straight line varies with velocity$\left(v\right)$ as $a=(1-v)$ $\mathrm{m} {\mathrm{s}}^{-2}$, where $v$ is in $\mathrm{m} {\mathrm{s}}^{-1}$. If initially the particle was at rest, then

A ball is projected vertically upwards from ground with velocity $v=24 \mathrm{m} {\mathrm{s}}^{-1}$. Assume the air resistance produces a constant retardation of $2 \mathrm{m} {\mathrm{s}}^{-2}$. Then $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A particle starts from rest and moves with acceleration $a=4\sin \left(\frac{\mathrm{\pi }t}{2}\right)\mathrm{m} {\mathrm{s}}^{-2}$ where $t$ is in seconds. Initially the particle is at origin and moves along $x$-axis, then

A particle starts moving along$\mathrm{x}$-axis from origin with initial velocity of $3 \mathrm{m} {\mathrm{s}}^{-1}$. The acceleration a of the particle varies with position $\mathrm{x}$ as $\mathrm{a}={\mathrm{Kx}}^2$, where $\mathrm{K}$ is a constant. At $\mathrm{x}=\sqrt{3} \mathrm{m}$, the tangent to the graph makes an angle of $60°$ with $\mathrm{x}$-axis. Then at $\mathrm{x}=\sqrt{3} \mathrm{m}$ ( $\mathrm{v}$ represents velocity of particle at position $\mathrm{x}$ )

A particle moves in a straight line with initial velocity ${\mathrm{u}}_0$. Retardation acting on the particle is$\mathrm{k} \mathrm{v}$, where $\mathrm{k}$ is a positive constant and $\mathrm{v}$ is instantaneous velocity. Then