A motorcyclist going at speed v suddenly finds a wide wall at a distance d ahead. The road friction can provide a maximum acceleration of exactly 2 d v 2 . Which manoeuvre can avoid the wall: braking in a straight line, or turning in a circle of radius d ?

Braking needs a 1 = 2 d v 2 , exactly the available friction, so it just succeeds. Turning needs a 2 = d v 2 = 2 a 1 , twice the available friction, so it fails. Only braking works.

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Physics - Circular Motion Question with Solution | TestHub

PhysicsCircular MotionDynamicsMedium2 minQB

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A motorcyclist going at speed $v$ suddenly finds a wide wall at a distance $d$ ahead. The road friction can provide a maximum acceleration of exactly $\frac{v ^{2}}{2 d}$ . Which manoeuvre can avoid the wall: braking in a straight line, or turning in a circle of radius $d$ ?

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Answer:

Solution:

Braking needs $a_{1} = \frac{v ^{2}}{2 d}$ , exactly the available friction, so it just succeeds.
Turning needs $a_{2} = \frac{v ^{2}}{d} = 2 a_{1}$ , twice the available friction, so it fails.
Only braking works.

Stream:JEESubject:PhysicsTopic:Circular MotionSubtopic:Dynamics

⏱ 2mℹ️ Source: QB

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