Stopping Distance of a Vehicle – Rankers Physics

Friction: Practice Problem & Solution

A vehicle of mass m is moving on a rough horizontal road with momentum P. If the coefficient of friction between the tyres and the road be \(\ \mu\), then the stopping distance is:
\(\frac{P}{2\mu mg}\)
\(\frac{P^2}{2\mu mg}\)
\(\frac{P}{2\mu m^2g}\)
\(\frac{P^2}{2\mu m^2g}\)

Solution Explained:

To solve this problem, we apply the core principles of Friction. Understanding the underlying formula is key to arriving at the correct answer below:

The stopping distance is given by \(s = \frac{v^2}{2a}\), where the frictional retardation is \(a = \mu g\). Substituting the relation for momentum \(v = \frac{P}{m}\) into the formula yields \(s = \frac{P^2}{2\mu m^2g}\).

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