Josef is late for a wedding and is speeding down a straight road at 145 km/hr when he passes an officer sitting in a police car parked behind a billboard at the side of the road. Two seconds after Josef's car passes him, the officer accelerates the police car from rest and maintains maximum acceleration of 8.5 km/hr s until he reaches a top speed of 210 km/hr. Eventually the officer gets within 150 m of the speeding vehicle and turns on the flashing lights. Josef sees the lights in his rearview mirror and panics, slamming on the brakes and starting to skid. Josef's car slows down at a rate of 5.5 m/s2. It takes the officer 0.5 seconds to realize what is happening and to move his foot to the brake pedal before he can start to slow down. The police car slows down at a rate of 6 m/s2.
(a) How long after Josef first passes the police car does it take before the officer turns on the flashing lights?
(b) How far has each vehicle traveled from the billboard when the officer turns on the flashing lights?
(c) Sketch of the position of both cars as a function of time on a single piece of graph paper, or use Excel. Clearly label your axes.
(d) How far apart are the two cars at the instant the officer starts to apply the brakes?
(e) Do the two vehicles collide? If so, at what speed (relative to Josef) does the police car strike Josef's vehicle? If not, what is the smallest distance that separates the two vehicles?

Question

Josef is late for a wedding and is speeding down a straight road at 145 km/hr when he passes an officer sitting in a police car parked behind a billboard at the side of the road. Two seconds after Josef's car passes him, the officer accelerates the police car from rest and maintains maximum acceleration of 8.5 km/hr s until he reaches a top speed of 210 km/hr. Eventually the officer gets within 150 m of the speeding vehicle and turns on the flashing lights. Josef sees the lights in his rearview mirror and panics, slamming on the brakes and starting to skid. Josef's car slows down at a rate of 5.5 m/s2. It takes the officer 0.5 seconds to realize what is happening and to move his foot to the brake pedal before he can start to slow down. The police car slows down at a rate of 6 m/s2.
(a) How long after Josef first passes the police car does it take before the officer turns on the flashing lights?
(b) How far has each vehicle traveled from the billboard when the officer turns on the flashing lights?
(c) Sketch of the position of both cars as a function of time on a single piece of graph paper, or use Excel. Clearly label your axes.
(d) How far apart are the two cars at the instant the officer starts to apply the brakes?
(e) Do the two vehicles collide? If so, at what speed (relative to Josef) does the police car strike Josef's vehicle? If not, what is the smallest distance that separates the two vehicles?

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