A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ‘t’ is proportional to

a) t^3/4

b) t^3/2

c) t^1/4

d) t^1/2

Force has a constant value. So acceleration is also constant..... So we can use it in that case.

Power=f.v =ma.v =m(v/t).(S/t) =m/t×s/t×s/t. {P=constant} 1=m{s^2/t^3} S^2=t^3 S=t^3/2Hence derivedThis is the simplest way I got the ans

Dear Student

Let's consider a body is moved along a straight line by a machine delivering a constant powerP. The distance moved by the body isS.
Power,P = F.v.. . . . . . (1)
Force,F = ma. . . . . . . .(2)

where,v = S/t​
acceleration,a = S/t²​
m =mass
From equation (1) and equation (2), we get
S²= Pt³/m​

From the above equation, we get
S² ∝ t³
S ∝ t^3/2
So option (B) is correct.

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya