A body of mass 8 kg,under the action of a fo | vedclass

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(B) Given the displacement equation: $s = \frac{t^2}{4}$.Velocity of the body: $v = \frac{ds}{dt} = \frac{d}{dt}(\frac{t^2}{4}) = \frac{2t}{4} = \frac

Vedclass · Accepted Answer

$16$

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(B) Given the displacement equation: $s = \frac{t^2}{4}$.Velocity of the body: $v = \frac{ds}{dt} = \frac{d}{dt}(\frac{t^2}{4}) = \frac{2t}{4} = \frac{t}{2} \ m/s$.Acceleration of the body: $a = \frac{dv}{dt} = \frac{d}{dt}(\frac{t}{2}) = \frac{1}{2} \ m/s^2$.Force acting on the body: $F = m 	imes a = 8 \ kg 	imes 0.5 \ m/s^2 = 4 \ N$.At $t = 0 \ s$,displacement $s(0) = 0 \ m$.At $t = 4 \ s$,displacement $s(4) = \frac{4^2}{4} = 4 \ m$.Work done by the force: $W = F 	imes \Delta s = 4 \ N 	imes (4 \ m - 0 \ m) = 16 \ J$.

$A$ body of mass $8 \ kg$,under the action of a force,is displaced according to the equation $s = \frac{t^2}{4} \ m$,where '$t$' is the time. Find the work done by the force in the first $4 \ s$. (in $J$)

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