First slide

Power

Question

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

Moderate

A

$t^{\frac{3}{4}}$
B

$t^{\frac{1}{4}}$
C

$t^{\frac{3}{2}}$
D

$t^{\frac{1}{2}}$

Solution

$p o w e r P = \frac{w o r k}{t i m e} P = \frac{F \cdot S}{t} P = F \cdot V P = f o r c e . v e l o c i t y$

$given P= F \cdot V = constant l e t c o n s \tan t = K F . V = K w e k n o w F = m a a n d v e l o c i t y = \frac{a c c e l e r a t i o n}{t i m e}, s u b s t i t u t e i n a b o v e e q u a t i o n$
$m \cdot a \cdot a t = K \Rightarrow a = {(\frac{K}{m t})}^{\frac{1}{2}} ---(!)$
$displacement S = \frac{1}{2} a t^{2} s u b s t i t u t e e q u a t i o n (1) \Rightarrow S = \frac{1}{2} a {(\frac{K}{m t})}^{\frac{1}{2}} t^{2}$
$\Rightarrow S = \frac{1}{2} {(\frac{K}{m})}^{\frac{1}{2}} t^{\frac{3}{2}}$
$∴ S α t^{\frac{3}{2}}$

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