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Work Energy and Power question

2012 · Q105
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Work Energy and Power question

2012 · Q105

NEETPhysicsWork Energy and PowerMCQ+4 / −1
A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to
  1. A
    t2P0
  2. B
    t1/2
  3. C
    t−-−1/2
  4. D
    tm{t \over {\sqrt m }}m​t​
View written solutionFree

Correct answer: B

Constant power of car P0 = F.V = ma.v

P0=mdvdt.v{P_0} = m{{dv} \over {dt}}.vP0​=mdtdv​.v

P0dt = mvdv Integrating

P0.t=mv22{P_0}.t = {{m{v^2}} \over 2}P0​.t=2mv2​

v=2P0tmv = \sqrt {{{2{P_0}t} \over m}} v=m2P0​t​​

∵\because∵ P0 , m and 2 are constant

∴\therefore∴ v∝tv \propto \sqrt t v∝t​

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