<p>You are driving at the speed of 33.4 m/s (74.7296 mph) when suddenly the car

Question

<p>You are driving at the speed of 33.4 m/s (74.7296 mph) when suddenly the car in front of you (previously traveling at the same speed) brakes. Considering an average human reaction, you press your brakes 0.484 s later. Assume that the brakes on both cars are fully engaged and that the coefficient of friction is 0.92 between both cars and the road. The acceleration of gravity is 9.8 m/s2 . <br /> a) Calculate the acceleration of the car in front of you when it brakes.<br /> b) Calculate the braking distance for the car in front of you.<br /> c) Find the minimum safe distance at which you can follow the car in front of you and avoid hitting it (in the case of emergency braking described here).</p>

Explanation / Answer

F = u m g = m a braking force where u = .92 a = u g = -9.02 m/s^2 2 a s = v^2 since the final speed is zero s = 33.4^2 / (2 * 9.02) = 61.9 m braking distance t = v/a = 33.4/9.02 = 3.7 sec time to decelerate to zero speed d = 33.4 * .484 = 16.2 m distance you will travel before braking Since both braking distances are the same you must be at least 16.2 m behind the car in front to stop in the same distance

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