A car is driving at a constant but unknown velocity. V0 on a straightaway. A mot

Question

A car is driving at a constant but unknown velocity. V0 on a straightaway. A motorcycle is a distance d behind the car. Initially, the both at the same velocity. The m starts to pass the car by speeding up at a constant acceleration a_m When the motorcyclist is side by side with the car, the motorcycle stops accelerating and is traveling at the velocity of the car. How long does the motorcycle accelerate? What was the initial velocity of the car and motorcycle? How far did the motorcycle travel while accelerating? A baseball is thrown from a cliff of height h by either dropping it to the bottom of the cliff, with an upward initial velocity v0 and downward with an initial velocity v0. Provide a sketch of the location as function of time. Calculate the time the baseball reaches the ground.

Explanation / Answer

(a)

for car

x = vo*t

for motorcyclist

x + d = v0*t + (1/2)*am*t^2

v0*t + d = v0*t + (1/2)*am*t^2

d = (1/2)*am*t^2

t = sqrt(2d/am)

(b)

for car vi = v0

for motorcycle vi = v0

(c)

distance = (vf^2 - vi^2)/(2*am) = ((2*v0)^2-v0^2)/(2*am) = v0^2/(2*am)

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