A body of mass 3kg is moving under the action of a force such that its displacement is given by the relation s=(1/3)t2 , where t is time in second. The work done by the force in 2s is

Question

A body of mass 3kg is moving under the action of a force such that its displacement is given by the relation s=(1/3)t2 , where t is time in second. The work done by the force in 2s is (A) (8/3) J (B) (19/5) J (C) (5/19) J (D) (3/8) J

Tardigrade Admin · Accepted Answer

s=(1/3)t2 v=(d s/d t)=(2/3)t,a=(d2 s/d t2)=(2/3) F=ma=3× (2/3)=2 N W= 2× (1/3)t2 At t=2 s , W=2× (1/3)× 2× 2=(8/3) J

Q. A body of mass $3 k g$ is moving under the action of a force such that its displacement is given by the relation $s = \frac{1}{3} t^{2}$ , where $t$ is time in second. The work done by the force in $2 s$ is

$\frac{8}{3} J$

$\frac{19}{5} J$

$\frac{5}{19} J$

$\frac{3}{8} J$

$s = \frac{1}{3} t^{2}$
$v = \frac{d s}{d t} = \frac{2}{3} t, a = \frac{d ^{2} s}{d t ^{2}} = \frac{2}{3}$
$F = ma = 3 \times \frac{2}{3} = 2 N$
$W = 2 \times \frac{1}{3} t^{2}$
At $t = 2 s$ ,
$W = 2 \times \frac{1}{3} \times 2 \times 2 = \frac{8}{3} J$

Q. A body of mass 3kg is moving under the action of a force such that its displacement is given by the relation s=31​t2 , where t is time in second. The work done by the force in 2s is

38​J

519​J

195​J

83​J