A car starts from rest and moves on a surface in which the coefficient of friction between the road and the tyres increases linearly with distance (). The car moves with the maximum possible accelerat

Question

A car starts from rest and moves on a surface in which the coefficient of friction between the road and the tyres increases linearly with distance (). The car moves with the maximum possible acceleration. The kinetic energy () of the car will depend on  as

Canvas Classes · Accepted Answer

🧠 Maximum Acceleration Is the Friction Limit — and KE Is the Work Friction Does

The car drives forward using friction, so the largest acceleration it can have is set by the available friction: . Here  grows linearly with distance, . So the driving force itself grows with , just like a spring force. The kinetic energy at distance  is the work this growing force has done.

🗺️ Working It Out

Maximum acceleration: .

Use . Integrating, .

So .

(Same result from work: .)

⚡ The Smart Move

A for

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