JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Work, Power & Energy

An automobile of mass '

m

' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:

Answer: (A)

Solution

Constant power delivered from rest gives the kinetic energy directly as

P t

\frac{1}{2} m v^{2} = P t \Rightarrow v = (\frac{2 P t}{m})^{1/2} = \frac{d x}{d t}

Integrating from the origin at

t = 0

x = (\frac{2 P}{m})^{1/2} \int_{0}^{t} t^{1/2} d t = \frac{2}{3} (\frac{2 P}{m})^{1/2} t^{3/2}

Taking the numerical factor inside the square root,

\frac{4}{9} \times \frac{2 P}{m} = \frac{8 P}{9 m}

, so the position is

x = (\frac{8 P}{9 m})^{1/2} t^{3/2}

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Single correct option