A body of mass $8\,kg$ is moved by a force $F = 3x\,N,$ where $x$ is the distance covered. Initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s.$ The final speed is ........... $m/s$
A body of mass $8\,kg$ is moved by a force $F = 3x\,N,$ where $x$ is the distance covered. Initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s.$ The final speed is ........... $m/s$
$6$
$12$
$18$
$14$
A body of mass $8\,kg$ is moved by a force $F = 3x\,N,$ where $x$ is the distance covered. Initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s.$ The final speed is ........... $m/s$
Increment in kinetic energy = work done
$⇒ \frac{1}{2}m({v^2} - {u^2}) = \int_{{x_1}}^{{x_2}} {F.dx} = \int_2^{10} {(3x)\;dx} $
$⇒ \frac{1}{2}m{v^2} = \frac{3}{2}[{x^2}]_2^{10} = \frac{3}{2}[100 - 4]$
$⇒ \frac{1}{2} \times 8 \times {v^2} = \frac{3}{2} \times 96$ $⇒$ $v = 6\,m/s$