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=‌at2Since acceleration
a=‌ (where
m is mass), we get:
s=‌×‌×t2Now, substitute
s from (ii) into our equation (i):
K=F×‌×‌×t2So,
K=‌t2We 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:
‌tA2=‌tB2You can cancel out
F2 and
‌ because they are the same:
‌=‌Rearrange to solve for time ratio:
‌=‌Take the square root for the ratio
tA:tB :
‌=√‌Plug in
mA=20kg and
mB=5kg :
‌=√‌=√4=2So, the ratio
tA:tB=2:1.