Question

The displacement of a body of mass $2kg$ varies with time t as $s=t^2+2t$, where s is in meters and t is in seconds. The work done by all the forces acting on the body during the time interval $t=2s$ to $t=4s$ is

Answer 1

Solution

We have,

$S=E^2+2t$

$V=\frac{ds}{dt}=\frac{\left(t^2\right)+2t}{dt}=2t+2$

At$t=2s,$

$vi=2t+2=2\left(2\right)+2=6h/s$

At $t=4s$

$Vf=2\left(4\right)+2=10m/s$

$△KE=\frac{1}{2}m[v{f}^2-v{i}^2]$

$△KE=\frac{1}{2}\times 2[100-36]=64J$

By work - Energy theorem,

$△w_{Forces}=△KE=64J$