Work Energy and Power

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:
‌

F2

2mA

tA2=‌

F2

2mB

tB2
You can cancel out F2 and ‌

1

2

because they are the same:
‌

tA2

mA

=‌

tB2

mB

Rearrange to solve for time ratio:
‌

tA2

tB2

=‌

mA

mB

Take the square root for the ratio tA:tB :
‌

tA

tB

=√‌

mA

mB

Plug in mA=20kg and mB=5kg :
‌

tA

tB

=√‌

20

5

=√4=2
So, the ratio tA:tB=2:1.