Question

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to`

• A. t^1/2
• B. t^3/4
• C. t^3/2
• D. t³

Answer 1

Answer: (A)

t^1/2

Answer 2

P = Fv = c

∴ $\frac{mdv}{v}v = c$

vdv = $\frac{cdt}{m}or\frac{v^{2}}{2} = \frac{ct}{m}$

(after integration)

$\left( \frac{ds}{dt} \right)^{2} = \frac{2ct}{m}or\left( \frac{ds}{dt} \right) = \sqrt{\frac{2c}{m}}t^{1/2}$

or s ∝ t^3/2