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66. 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 ?

66. 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 ?

Grade:12

1 Answers

SAHIL
3778 Points
7 years ago
Distance travelled,s = ut +1/2a(t^2) where u=initial velocity, a =acceleration, t=time 

Assuming u= 0 
s=1/2a(t^2) 
F=ma 
F = power/velocity 
P/v =ma , but P and m are constant so; 
1/v is proportional to a 
v =s/t 
1/v =t/s 
t/s proportional to a 
Substitute t/s for a in s=1/2a(t^2) 
s is proportional to (t/s) *(t^2) 
s is proportional to (t^3)/s 
so s^2 is proportional to t^3 
and s is proportional to t^3/2

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