Question

A force given by the relation $F=8t,$ acts on a body of mass $2kg$ , initially at rest. Find the work done by this force on the body during first $2$ seconds of its motion.

• A. $64J$
• B. zero
• C. $-64J$
• D. none of these

Answer 1

Answer: (A)

$F=ma=8t$
$a=8t$
$\frac{d v}{d t}=8t$
$dv=8tdt$
$\displaystyle \int _{0}^{v}dv=\displaystyle \int 8tdt$
$\frac{8 t^{2}}{2}=\left|4 t^{2}\right|_{0}^{2}$
$V=16ms^{- 1}$
$w=\Delta K$
$=\frac{1}{2}\times \left(\right.2\left.\right)\left(\left(16\right)^{2} - 0\right)$
$=64J$