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A body at rest is moved along a horizont...

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

A

`t^((3)/(2))`

B

`t^((1)/(2))`

C

`t^((3)/(4))`

D

`t^((1)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
A
P= constant
`(1)/(2) mv^(2)= Pt`
`rArr v prop sqrtt`
`(dx)/(dt)= C sqrtt` {`because` C= constant}
By integration, `x= C (t^((1)/(2)+1))/((1)/(2)+1) rArr x prop t^(3//2)`
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