A body of mass 3 kg acted upon by a constant force is displaced by S metre, given by relation S=(1/3)t2, where t is in second. Work done by the force in 2 is

Question

A body of mass 3 kg acted upon by a constant force is displaced by S metre, given by relation S=(1/3)t2, where t is in second. Work done by the force in 2 is (A)  (8/3)J  (B)  (19/5)J  (C)  (5/19)J  (D)  (3/8) J

Tardigrade Admin · Accepted Answer

Given that, S=(1/3) t2 v=(d S/d t)=(2/3) t ; a=(d2 S/d t2)=(2/3) F=m a=3 × (2/3)=2 N ; Work =2 × (1/3) t2 At t=2 Work =2 × (1/3) × 2 × 2=(8/3) J

Q. A body of mass $3 k g$ acted upon by a constant force is displaced by $S$ metre, given by relation $S = \frac{1}{3} t^{2},$ where $t$ is in second. Work done by the force in $2$ is

$\frac{8}{3} J$

$\frac{19}{5} J$

$\frac{5}{19} J$

$\frac{3}{8} J$

Given that, $S = \frac{1}{3} t^{2}$
$v = \frac{d S}{d t} = \frac{2}{3} t; a = \frac{d ^{2} S}{d t ^{2}} = \frac{2}{3}$
$F = ma = 3 \times \frac{2}{3} = 2 N;$ Work $= 2 \times \frac{1}{3} t^{2}$
At $t = 2$
Work $= 2 \times \frac{1}{3} \times 2 \times 2 = \frac{8}{3} J$

Q. A body of mass 3kg acted upon by a constant force is displaced by S metre, given by relation S=31​t2, where t is in second. Work done by the force in 2 is

38​J

519​J

195​J

83​J