Question

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 2.0 s after the car has passed the stop sign. She accelerates at 4.2 m/s^2 until her speed is 110 km/h, and then continues at this speed until she catches the car. At that instant,the car is 1.4km 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? (Ans:52 s, 98 km/h). Explain in detail how to solve.

Answer 1

Let be the time taken by the officer to catch the car after the car has passed the stop sign.

Given that when the officer catches the car, it had traveled a distance of 1.4km

Total distance,

The officer also had to cover the same distance to catch the car.

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Consider the officer on the motorcycle

Consider the accelerating part after starting from rest

Final velocity,

To convert km/h to m/s. Divide by 3.6

Use the formula to find the time taken for accelerating

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Distance covered while accelerating

Use formula

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The remaining distance is covered at a constant velocity of 110km/h

Remaining distance,

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Speed = Distance/Time

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Total time taken by the officer

Given that the police officer takes off in pursuit 2.0 s after the car has passed the stop sign.

So

(a) ANSWER:

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(b) How fast was the car traveling?

The car was travelling at a constant speed

Speed = Distance/Time

To convert m/s to km/hr. Multiply by 3.6

(b) ANSWER:

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