Question

Given curve is $\frac{1}{v}$ versus x for a particle under motion is, where v is velocity and x is position. The time taken in seconds by particle to move from x = 4 to x = 12 m is (Given - particle is at origin at t = 0)

Answer 1

Curve is passing through origin,
$\therefore$ equation of the curve will be of the form y = mx,
$\frac{1}{v}=\frac{1}{8}.x$
$\Rightarrow \frac{dt}{dx}=\frac{1}{8}x$
$\Rightarrow 8\int dt=\int xdx$
$\Rightarrow 8t=\frac{x^2}{2}+c$
As at t = 0, x = 0, $\therefore c=0$
$\therefore 8t=\frac{x^2}{2}\Rightarrow x^2=16t$
$\therefore$ Time taken to move from x = 4 to x = 12 m
$=\frac{144}{16}-\frac{16}{16}=9-1=8s$