Question

A time dependent force $F =8 t$ acts on an object of mass $2\, kg$. If the object starts from rest, the work done by the force during the first $4\, s$ will be __________$J$.

Answer 1

From Newton's second law,
$F =8 t = ma$
$\therefore 2 a =8 t$
$\therefore \frac{ dv }{ dt }=4 t$
$\therefore \int\limits_{0}^{ v } dv =\int\limits_{0}^{4} 4 t dt$
$\therefore v =\left(2 t ^{2}\right)_{0}^{4}$
$\therefore v =32\, m / s$
From work energy theorem,
$W _{ F }=\Delta K . E .=\frac{1}{2} m \left( v ^{2}- u ^{2}\right)$
$=\frac{1}{2} 2(1024-0)$
$\therefore W _{ F }=1024\, J$