Question

the displacement of a body of mass 2 kg varies with time 't' as s=t*2+2t whede s is in matrea and 't' is in seconds. the work done by all the forces acting on the body during the time interval t = 2s to 4s is

Answer 1

Given s=t2+2t→v=dsdts=t2+2t→v=dsdt=d(t2+2t)dt=d(t2+2t)dt=2t+2=2t+2

⇒Kf=12⇒Kf=12 mv2fmvf2=12=12×2(2×4+2)2×2(2×4+2)2=100J=100J

⇒Ki=12⇒Ki=12 mv2imvi2=12=12×2(2×2+2)2×2(2×2+2)2=36J=36J

⇒W=Kf−Ki=100−36=64J

Answer 2

Mass of the body = 2 kg

Displacement is given by the equation:

$s = t^2 + 2t$

$v = 2t + 2$

$a = \frac{\delta v}{\delta t} =2$

Force = 2 × 2 = 4 N

Now, we need to find displacement between t = 2 to t = 4 seconds

s(2) = 4 + 4 = 8 m

s(4) = 16 + 8 = 24 m

Displacement = 24 - 8 = 16 m

Work done = Force × displacement

Work done = 4 × 16 = 64 Joules

Hence, the work done is 64 Joules

Option B is correct.