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  4. A body of mass 3 kg acted upon by a constant force is displaced by S metre, given by relation S=(1/3)t2, where t is in second. Work done by the force in 2 is

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Q. A body of mass $3 \,kg$ acted upon by a constant force is displaced by $S$ metre, given by relation $ S=\frac{1}{3}t^{2}, $ where $t$ is in second. Work done by the force in $2$ is

WBJEEWBJEE 2008Work, Energy and Power

Solution:

Given that, $S=\frac{1}{3} t^{2}$
$v=\frac{d S}{d t}=\frac{2}{3} t ; a=\frac{d^{2} S}{d t^{2}}=\frac{2}{3}$
$F=m a=3 \times \frac{2}{3}=2 N ;$ Work $=2 \times \frac{1}{3} t^{2}$
At $t=2$
Work $=2 \times \frac{1}{3} \times 2 \times 2=\frac{8}{3} J$