The displacement of a body of mass 2 kg varies with time t as S =t2 + 2t, where S is in meters and t is in seconds. The work done by all the forces acting on the body during the time interval t = 2 s to t = 4 s is

Question

The displacement of a body of mass 2 kg varies with time t as S =t2 + 2t, where S is in meters and t is in seconds. The work done by all the forces acting on the body during the time interval t = 2 s to t = 4 s is (A) 36 J (B) 64 J (C) 100 J (D) 120 J

Tardigrade Admin · Accepted Answer

v=(dS/dt)=2t + 2 From work energy theorem; W textnet =Δ K.E. =Kf-Ki =(1/2)m(v2f-v2i) =(1/2) × 2[(2 × 4 +2)2-(2 × 2+2)2]= 64 J

Q. The displacement of a body of mass $2 k g$ varies with time $t$ as $S = t^{2} + 2 t$ , where $S$ is in meters and t is in seconds. The work done by all the forces acting on the body during the time interval $t = 2 s$ to $t = 4 s$ is

36 J

64 J

100 J

120 J

$v = \frac{d S}{d t} = 2 t + 2$

From work energy theorem;

$W_{net} = Δ K . E . = K_{f} - K_{i}$

$= \frac{1}{2} m (v_{f}^{2} - v_{i}^{2})$

$= \frac{1}{2} \times 2 [(2 \times 4 + 2)^{2} - (2 \times 2 + 2)^{2}] = 64 J$

Q. The displacement of a body of mass 2kg varies with time t as S=t2+2t, where S is in meters and t is in seconds. The work done by all the forces acting on the body during the time interval t=2s to t=4s is