Question

The plot of velocity versus time graph for a particle moving along a straight line is shown.

The value of dot product of velocity and acceleration of particle at $t=2s$ is

• A. $1m^2/s^3$
• B. $-1m^2/s^3$
• C. $2m^2/s^3$
• D. $-2m^2/s^3$

Answer 1

The correct option is B $-1m^2/s^3$

We know that acceleration from $v-t$ graph is given by the slope of $v-t$ graph
$⟹a=\frac{dv}{dt}=\tan {45}^{\circ }=1m/s^2$.
From $v-t$ graph
At $t=3s,v=0$
Using first equation of motion, we can say
$v=u+at$
$\Rightarrow 0=u+\left(1\right)\left(3\right)$
$\therefore$ Initial velocity of the particle $u=-3m/s$
At $t=2s$
$v=-3+1\times 2=1m/s$
$\therefore v=-1m/s$
We know that, acceleration at $t=2s$ is $a=1m/s^2$
$\therefore$ Dot product of $v$ and $a$ at $t=2s\text{is}\overrightarrow{v}.\overrightarrow{a}=-1m^2/s^3$