First slide

Work done by Diff type of forces

Question

A body of mass 3 kg is under a force which causes a displacement in it, given by s =t² / 3 (in m). Find the work done by the force in 2 second

Difficult

A

2j
B

3.8j
C

5 .2j
D

2.6 j

Solution

$\begin{array}{l} W = \int_{0}^{2} F \cdot ds = \int_{0}^{2} mads \\ = \int_{0}^{2} m \cdot \frac{d^{2} s}{{dt}^{2}} \cdot \frac{ds}{dt} \cdot dt \\ = \int_{0}^{2} 3 (\frac{2}{3}) (\frac{2}{3} t) dt \\ = \frac{4}{3} \int_{0}^{2} tdt = \frac{4}{3} {[\frac{t^{2}}{2}]}_{0}^{2} \\ = \frac{4}{3} \times \frac{4}{2} = \frac{8}{3} = 2 \cdot 6 J \end{array}$

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