Question

The relation b t w displacement & times t for a body g man 2 Kg moving levels the certain of a force is given by $X=\frac{t^3}{3}$ calculate the work done by the object in the.

Answer 1

Given that,

Mass of body $M=2Kg$

Displacement $x=\frac{t^3}{3}$

$\frac{dx}{dt}=t^2$

$dx=t^{2}dt..........\left(1\right)$

$\because v=\frac{dx}{dt}=t^2$

$a=\frac{dv}{dt}=2t$

Work done

$W=force\times displacement$

$W=ma\times dx$

$W=2\times 2t\times t^{2}dt$

$W=4t^{3}dt$

$W=t^4$