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A 1.50 multiplied by 103 kg car starts from rest and accelerates uniformly to 19.9 m/s in 11.6 s. Assume that air resistance remains constant at 400 N during this time.
(a) Find the average power developed by the engine.
1 W

(b) Find the instantaneous power output of the engine at t = 11.6 s, just before the car stops accelerating

  • physics -

    (a) Paverage*t = Kinetic energy increase + work done against air friction.
    KE increase = 297,000 J
    t = 11.6 s
    distance traveled = X = (19.9/2)*11.6 = 115.4 m

    The work done against friction = 400N*115.4m = 46,170 J

    Pav*t = 343,170 J
    Pav = 29,584 W

    The assumption of constant air friction is completly unrealistic and will underestimate the final instantaneous power level.

    You can come up with an answer by using the instantaneous relation
    P = (Force)*(Velocity)

    For the force, add the air resistance to the force required to accelerate,
    F @ t=11.6s = M*a + 400 N
    = 2573 + 400 = 2973 N
    Instantaneous power = F*V = 59,168 W

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