How Fast Can the Police Motorcycle Catch Up with the Speeding Car?
How much time elapses before the motorcycle is moving as fast as the car?
A car is traveling at a steady 71 km/h in a 50 km/h zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady 7.4 m/s². How long will it take for the police motorcycle to catch up with the car?
Answer:
The police motorcycle takes about 2.67 seconds to reach the speed of the car which was moving at 71 km/h in a 50 km/h zone.
Explanation:
The situation described in this scenario involves the concepts of speed, time, and acceleration in physics. The car is initially moving at 71 km/h, which is equivalent to 19.72 m/s. The police motorcycle starts from rest and accelerates at 7.4 m/s².
To calculate the time it takes for the motorcycle to catch up with the car, we use the formula for acceleration: final velocity minus initial velocity over time. Since the initial velocity of the motorcycle is 0 m/s, we need to find the time (t) it takes for the motorcycle to reach a speed of 19.72 m/s (same as the car).
Using the formula: (19.72 m/s - 0 m/s) / 7.4 m/s² = 2.67 seconds. Therefore, approximately 2.67 seconds elapse before the motorcycle is moving as fast as the car.