Question

The figure shows the plot of velocity $\left(v\right)$ versus time $\left(t\right)$ on a log–log scale. Assuming straight line motion and the particle to start from origin, the distance $\left(inmeter\right)$ covered at the end of $t=3s$ is

• A. $6$
• B. $2$
• C. $9$
• D. $4$

Answer 1

The correct option is C $9$

From above diagram equation of straight line is given by

$y=mx+c$
Here, $m=\tan {45}^{\circ }=1$
$\text{log}v=1\left(\text{log}t\right)+\text{log}2$
$\text{log}v=\text{log}2t$
$v\left(t\right)=2t$
From $v\left(t\right)=\frac{dx}{dt}$
Particle start from origin, $x_i=0$
${\int }_0^{x}dx={\int }_0^{t}vdt$
$x={\int }_0^{t}2tdt$
$x=t^2$
Distance covered in $t=3s$
$x=9m$
Final Answer: (a)