Question

A body of mass $8\, kg$ is moved by a force $F=3 \times N$, where $x$ is the distance covered. Initial position is $x-2 m$ and the final position is $x=10\, m$. 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, $F=m a=m \frac{d v}{d t}$
$3 x=8 \frac{d v}{d x} \cdot \frac{d x}{d t}$
$3 x=8 v \frac{d v}{d x}\left[\because \frac{d x}{d t}=v\right]$
$3 x d x=8 v d v$
Integrating both sides
$3\left[\frac{x^{2}}{2}\right]_{2}^{10}=8\left[\frac{v^{2}}{2}\right]_{0}^{v}$
$\frac{3}{2}\left[10^{2}-2^{2}\right]=4 v^{2}$
$\frac{3}{2} \times 96=4 v^{2}$
$v =6\, m / s$