(D) Given: Mass $m = 3 \,kg$,displacement $s = \frac{t^3}{3}$.Velocity $v = \frac{ds}{dt} = \frac{d}{dt}(\frac{t^3}{3}) = t^2$.Acceleration $a = \frac

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(D) Given: Mass $m = 3 \,kg$,displacement $s = \frac{t^3}{3}$.Velocity $v = \frac{ds}{dt} = \frac{d}{dt}(\frac{t^3}{3}) = t^2$.Acceleration $a = \frac{dv}{dt} = \frac{d}{dt}(t^2) = 2t$.Force $F = ma = 3 \times 2t = 6t$.Work done $W = \int F \cdot ds = \int_0^2 F \cdot v dt = \int_0^2 (6t)(t^2) dt$.$W = \int_0^2 6t^3 dt = 6 \left[ \frac{t^4}{4} \right]_0^2$.$W = 6 \times \frac{16}{4} = 6 \times 4 = 24 \,J$.

Class 11 Physics Work, Energy, Power and Collision Work Done by Variable Force and Force-Displacement Graph

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The displacement $s$ of a body of mass $3 \,kg$ under the action of a force is given by $s = \frac{t^3}{3}$,where $s$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is (in $\,J$)

TS EAMCET 2023 All TS EAMCET

A
$32$
B
$3.8$
C
$5.2$
D
$24$

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Work Done by Variable Force and Force-Displacement Graph

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The displacement $s$ of a body of mass $3 \,kg$ under the action of a force is given by $s = \frac{t^3}{3}$,where $s$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is (in $\,J$)

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