First slide

Work Energy Theorem

Question

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

Moderate

A

64 J
B

zero
C

$- 64 J$
D

none of these

Solution

F = ma = 8t
a = 8t
$\frac{dv}{dt} = 8 t$
$dv = 8 tdt$
$\int_{0}^{v} dv = \int 8 tdt$
$\frac{8 t^{2}}{2} = {|4 t^{2}|}_{0}^{2}$
$V = 16 {ms}^{- 1}$
$w = Δ K$
$= \frac{1}{2} \times (2) (16^{2} - 0)$ = 64 J

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