If the braking distance for your car at a certain speed is 200 ft and, after reacting to a situation, you have managed to stop your car in 5.0 s, then the magnitude of the acceleration was A) 16 ft/s². B) 25 ft/s². C) 32 ft/s². D) 50 ft/s².

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Quizplus · Accepted Answer

The acceleration is given by the formula a = (v^2 - u^2) / 2s, where v is the final velocity, u is the initial velocity, and s is the distance traveled. In this case, the final velocity is 0 ft/s, the initial velocity is the speed at which the car was traveling before braking, and the distance traveled is 200 ft. Substituting these values into the formula, we get a = (0^2 - u^2) / 2(200) = -u^2 / 400. Since the car is braking, the acceleration is negative, so we can rewrite the equation as a = u^2 / 400. To find the magnitude of the acceleration, we take the absolute value of this expression, which gives us |a| = u^2 / 400. We don't know the exact value of u, but we can use the fact that the car stopped in 5.0 s to find a lower bound for u. The average velocity of the car during braking is given by v = (u + v) / 2, where v is the final velocity. Since the final velocity is 0 ft/s, we have v = u / 2. The average velocity is also given by v = s / t, where s is the distance traveled and t is the time taken. Substituting these values into the equation, we get u / 2 = 200 / 5 = 40 ft/s. Substituting this value into the expression for the magnitude of the acceleration, we get |a| = (40 ft/s)^2 / 400 = 16 ft/s^2.

If the Braking Distance for Your Car at a Certain