Question

A body is moved along a straight line by a machine delivering constant power . The distance moved by the body is time `t` is proptional to
A. `t^(1//2)`
B. `t^(3//4)`
C. `t^(3//2)`
D. `t^(2)`

Answer 1

Correct Answer - C
(c ) ` p= (E )/(t) = constt` :. ((1)/(2)mv^(2))/(t) = `constt
`rArr (v^(2))/(t) = `constt (k) :. V = kt^(1//2) `and `(dx)/(dt) = kt^(1//2)`
or , `ds = kt^(1//2) dt`
By integrating we get
`rArr s = (2kt^(3//2))/(3) + C rArr s prop t^(3//2)`