Two bodies A and B of masses 20 kg and 5 kg respectively are at rest. Due to the action of a force of 40 N separately, if the two bodies acquire equal kinetic energies in times tA and tB respectively, then tA:tB=
Let's use the work-energy theorem, which says: K‌=W ⇒‌‌K‌=F×s‌‌...(i) Here, K is kinetic energy, F is force, and s is distance. When a force acts and the body starts from rest, the distance s covered in time t is: s=‌
1
2
at2 Since acceleration a=‌
F
m
(where m is mass), we get: s=‌
1
2
×‌
F
m
×t2 Now, substitute s from (ii) into our equation (i): K=F×‌
1
2
×‌
F
m
×t2 So, K=‌
F2
2m
t2 We are told both bodies A and B get the same kinetic energy ( KA=KB ) using the same force F=40N, but their masses and times are different. Set up the equation for both bodies and compare: ‌