39. | a car is traveling at a steady 80 km/h in a 50 km/h zone. a
police motorcycle takes off at the instant the car passes it, accel-
erating at a steady 8.0 m/s².
a. how much time elapses before the motorcycle is moving as
fast as the car?
b. how far is the motorcycle from the car when it reaches this
speed?

a) 2.8 s b) 30.8 m

Explanation:

a) For a uniform acceleration a the equation for velocity v is given by:

For the police car the given values are:

v₀ = 0, v = 80 km/h = 22.2 m/s , a = 8 m/s²

Solving for time t:

b) In this time t the distance x traveled by the car with uniform velocity v is given by:

For the car the given values are:

v = 80 km/h = 22.2 m/s, x₀ = 0, t = 2.8 s

x = 61.7

The distance s traveled by the police car with uniform acceleration a is:

The given values are:

a = 8m/s², v₀ = 0, x₀ = 0, t = 2.8 s

s = 30.9 m

The difference between the distance x traveled by the car and the distance s traveled by the police is 30.8 m

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