An automobile of mass m accelerates starting from the origin and initially at rest, while the engine…

An automobile of mass m accelerates starting from the origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:
  1. 9P8 m12t32
  2. 8P9 m12t23
  3. 9m8P12t32
  4. 8P9 m12t32

Solution

P=const

P=FV=mv2 dvdx

∫0xPmdx=∫0vv2 dv

Pxm=v33

3Pxm13=v=dxdt

3Pm13∫0tdt=∫0xx-13dx

⇒x=8P9 m12t32

Asked in: JEE Main 2021 (27 Jul Shift 2)

Practice more Work Power Energy questions on Aicharya