Question

A body of mass 3kg is under a forace which causes a displacement in it givan by S=2t/3( inm) find the work Done by the force is first 2 sec

a) 2j b)3.8j c)24j d)29​

Answer 1

CORRECT QUESTION :

A body of mass 3kg is under a force which causes a displacement in it given by S=2t/3 ( in m). find the work done by the force in first 2 sec.

ANSWER :

Option c) 24 J.

GIVEN :

• Mass of a body, m = 3 kg.
• Displacement, $\sf S \: = \: \dfrac {2t}{3}$

TO FIND :

• Work done by the force in first 2 seconds.

SOLUTION :

$\implies \sf \dfrac {t^{3}}{3}$

$\implies \sf \dfrac {ds}{dt} \: = \: t^{2}$

$\implies a \: = \: 2 t$

$\implies w \: = \: \int fd$

$\implies \displaystyle \int_{0}^{2} mat^{2}dt$

$\implies \displaystyle 3\int_{0}^{2} 2t^{3}dt$

$\implies \displaystyle 6\int_{0}^{2} t^{3}dt$

$\implies \sf \dfrac{6}{4}\big[t^{4}\big]_{0}^{2}$

$\implies \sf \dfrac {6}{4} \: \times \: 16$

$\implies \sf = 6 \: \times \: 4$

$\therefore {\boxed {\sf w \: = \: 24 \: J}}$

•°• Therefore, work doen by the force in first two sec is 24 J.