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

Options

A. (a) ` t^^(1//2)`
B. (b) ` t^(3//4)`
C. (c ) ` t^(3//2)`
D. (d) `t^2`

Answer

C

Explanation

Power= force xx velocity `= F xx v =ma xx c`
` =m (dv)/(dt) v or ` (v dv)/(dt) = a constant =c` ltbRgt or ` v dv= c dt` Integrating it, we have
v^2/2 =ct ` or ` v= sqrt 2 ct^(1//2) = C_1 t^(1//2)`
or ` (dx)/(dt) = C_1 t^(1//2) or ` dx= C_1 t^(1//2) dt`. Integrating it,
we get ` x= 2/3 C_1t^(1//2)` or ` x prop t^(3//2)`.