**AP Physics 1 Question 286: Answer and Explanation**

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**Question: 286**

**4.** A car of mass 1000 kg is traveling at a speed of 5 m/s. The driver applies the breaks, generating a constant friction force, and skids for a distance of 20 m before coming to a complete stop. Given this information, what is the coefficient of friction between the car's tires and the ground?

- A. 0.25
- B. 0.2
- C. 0.125
- D. 0.0625

**Correct Answer:** D

**Explanation:**

**D**

First, you know *F*_{f} = μ*F*_{N} = µ(*mg*). Second, you know that *W* = Δ*KΕ* = *KE*_{f} - *KE*_{0} = -*KE*_{0} (since *KE*_{f} = 0 in this case) = - *mv*_{0}^{2}. Plugging in numbers, you get *W* = - (1000 kg)(5 m/s)^{2} = -12,500 J. You also know that *W* = *Fd*cos*θ* = [µ(*mg*)]*d*cos*θ*. Solving for μ, you get μ = *W*/[(*mg*)*d*cos*θ*]. Plugging in the numbers then gives μ = -12,500 J/[(1000 kg)(10 m/s^{2})(20 m)(cos180°)] = 0.0625.