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In the class we saw how the power, P (constant) is delivered to a car, of...

In the class we saw how the power, P (constant) is delivered to a car, of mass m, by its motor, based on it:
a) Show that the distance traveled in a time t by the car, starting from rest, is given by. x = sqrt (8P / 9m) * t ^ (3/2)
b) Make the corresponding graphs of the position against the time for the car when the power developed is P = 800W, P = 400W and P = 200W. Keep in mind that at rest the car exerts a constant force, on the ground of the street, of 1.6 * 10 ^ 4 N
c) According to the graphs of position against time (from the previous part) How is the movement of the car described? Explain your answer
d) Make a graph of Speed ??against time
e) Is this problem of constant acceleration? Explain your answer
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