CGPET 2019 Solved Paper

Given power, P=3t2−2t+1
We know that, P=

dW

dt

.......(i)
⇒dW=Pdt
and from work energy theorem,
Work down, dW=Kf−Ki=ΔK ........(ii)
From Eqs. (i) and (ii)
ΔK=Pdt
⇒ΔK=

4

∫

2

Pdt
=

4

∫

2

(3t2−2t+1)dt
=[

3t3

3

−

2t2

2

+t]24
=(t3−t2+t)24=[(4)3−(4)2+(4) −(2)3+(2)2−2] =64−16+4−8+4−2=46J
So, the change in its kinetic energy between t=2s and t=4s is 46J.