Question

The given graph is $\frac{1}{\text { acceleration }(a)}$ vs velocity $(v)$ graph. If the time interval during which velocity changes from $2 m / s$ to $4 m / s$ is given by $\Delta t$ seconds, then find the value of $2 \Delta t$.

Answer 1

$\frac{1}{a}=\frac{1}{4} v$
$\frac{d t}{d v}=\frac{1}{4} v ; \int\limits_{t_{1}}^{t_{2}} d t=\int\limits_{2}^{4} \frac{v}{4} d v$
$t_{2}-t_{1}=\frac{1}{4} \times \frac{1}{2}[16-4]=\frac{3}{2} s$