A body of mass 2 kg is moving along the x-di | vedclass

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(C) Given: $m = 2 \ kg$, $x(t) = t^2 + t + 1 \ m$.The velocity is $v(t) = \frac{dx}{dt} = 2t + 1 \ m/s$.The acceleration is $a(t) = \frac{dv}{dt} = 2

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$24$

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(C) Given: $m = 2 \ kg$, $x(t) = t^2 + t + 1 \ m$.The velocity is $v(t) = \frac{dx}{dt} = 2t + 1 \ m/s$.The acceleration is $a(t) = \frac{dv}{dt} = 2 \ m/s^2$.Since the acceleration is constant, the force acting on the body is $F = m 	imes a = 2 \ kg 	imes 2 \ m/s^2 = 4 \ N$.The displacement $s$ during the interval $t = 2 \ s$ to $t = 3 \ s$ is $s = x(3) - x(2)$.$x(3) = (3)^2 + 3 + 1 = 9 + 3 + 1 = 13 \ m$.$x(2) = (2)^2 + 2 + 1 = 4 + 2 + 1 = 7 \ m$.$s = 13 - 7 = 6 \ m$.The work done is $W = F 	imes s = 4 \ N 	imes 6 \ m = 24 \ J$.

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