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1. Homework Statement

1. Homework Statement

A motorcycle officer hidden at an intersection observes a car driven by an oblivious driver who ignores a stop sign and continues through the intersection at constant speed. The police officer takes off in pursuit 1.58 s after the car has passed the stop sign. She accelerates at 4.5 m/s2 until her speed is 119 km/h, and then continues at this speed until she catches the car. At that instant, the car is 1.9 km from the intersection.

(a) How long did it take for the officer to catch up to the car?

(b) How fast was the car traveling?

## Homework Equations

x(t) = x0 + v0 + 0.5at^2

v(t) = v0 + at

## The Attempt at a Solution

So first I would list and convert the values given.

t = 1.58 s

a = 4.5 m/s

vf = 119 km/h ≈ 33 m/s

xf = 1.9 km = 1900 m

I spoke with my professor on this and he said to divide the sections to when the police officer was at rest, when the officer actually takes off, and when the police officer has caught the speeder.

I'm really clueless on how to go through this so I'll just try here.

v(t) = v0 + (4.5)(1.58)

v(t) = 0 + 7.11

v(t) = 7.11 m/s

x(t) = 0 + (7.11)(1.58) + 0.5(4.5)(1.58)^2

x(t) = 16.85 m