First slide

Work done by Diff type of forces

Question

A force of $F = 10 t + 3 t^{2}$ is acting on a particle on a particle of mass 1Kg at rest, where F is in newton and t is in seconds. Work done by this force in first 1 second is

Moderate

A

18 J
B

14 J
C

32 J
D

36 J

Solution

$\begin{array}{l} F = 10 t + 3 t^{2} m \frac{d v}{d t} = 10 t + 3 t^{2} d v = (10 t + 3 t^{2}) d t \\ v = {|\frac{10 t^{2}}{2} + t^{3}|}_{0}^{1} \\ v a f t e r 1 s e c 6 m / s . \\ w o r k d o n e i s e q u a l t o c h a n g e i n K . E = \frac{1}{2} (1) {(6)}^{2} = 18 J \end{array}$

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