1. A car\'s maximum acceleration can be modeled very accurately if you know the

Question

1. A car's maximum acceleration can be modeled very accurately if you know the power that it's engine can produce as a function of time. The car's velocity is then 2Pt 0 where P is the power generated by a car's engine and m is the mass of the car. For a certain car m = 820 kg and P-31000 W. If the car starts from rest at time t = 0 s, how far can this car travel in 5 s? 2. For problem 1 create plots (using a computer) of the car's acceleration, velocity, and position as functions of time from t = 0 to t = 100 s.

Explanation / Answer

Solution:

Let us go to the basics first.

Velocity of car after 5 seconds is given by eqn.1 stated in the problem:

V = (2Pt/m)

=>V = (2*31000*5 / 820) = 19.443 m/s

u=initial velocity = 0 (since given car was at rest)

Thus, acceleration, a = (V - u ) / t = (19.443 – 0)/5 = 3.89 m/s2

Thus, from Newton’s eqn:

V2 = u2 + 2aS      (where S = distance)

=>19.4432 = 0 + 2*3.89S

=>S = 48.6 m          (Answer)

Thanks!!!

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