Question

A body of mass $8kg$ is moved by a force $F=3\times N$, where $x$ is the distance covered. Initial position is $x-2m$ and the final position is $x=10m$. The initial speed is zero. The final speed is

• A. 6 m / s
• B. 12 m / s
• C. 18 m / s
• D. 14 m / s

Answer 1

Answer: (A)

Force, $F=ma=m\frac{dv}{dt}$
$3x=8\frac{dv}{dx}\cdot \frac{dx}{dt}$
$3x=8v\frac{dv}{dx}\left[\because \frac{dx}{dt}=v\right]$
$3xdx=8vdv$
Integrating both sides
$3{\left[\frac{x^2}{2}\right]}_2^{10}=8{\left[\frac{v^2}{2}\right]}_0^v$
$\frac{3}{2}\left[10^2-2^2\right]=4v^2$
$\frac{3}{2}\times 96=4v^2$
$v=6m/s$