Multiple choice

A $1500 kg$ car is initially moving with speed $30 {m}/{s}$. Suddenly, a rock falls onto the road ahead. The maximum coefficient of friction between the car tires and the roads is $\mu = 0.7$. Approximately how much distance will the car need to stop to avoid hitting the rock?

  1. $22 m$
  2. $46 m$
  3. $66 m$
  4. $87 m$
  5. $131 m$
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C Correct answer
Explanation

Using the work-energy theorem, the kinetic energy 1/2 * m * v^2 is dissipated by friction force f * d = mu * m * g * d. Thus, 1/2 * v^2 = mu * g * d. d = v^2 / (2 * mu * g) = 30^2 / (2 * 0.7 * 9.8) = 900 / 13.72 = 65.59 m, which is approximately 66 m.

AI explanation

Using the kinematic equation v squared equals u squared plus 2as, the final velocity v is zero and the initial velocity u is 30 m/s. The maximum deceleration is the coefficient of friction multiplied by g, which is 0.7 times 10 m/s squared, equalling 7 m/s squared. Setting up the equation gives zero equals 30 squared minus 2 times 7 times s, meaning 900 equals 14s. Solving for s gives approximately 64.3 meters, which is closest to 66 meters.

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