How do you determine the minimum stopping distance of a motorcycle, given its velocity and the kinetic coefficient of friction?

A motorcycle moving at 25.0m/s slides to a stop. Calculate the minimum stopping distance if the kinetic coefficient of friction between the tire and the road is 0.7.

1 Answer
Matt
Apr 15, 2016

Minimum stopping distance = 45.49m

Explanation:

The friction between the bike and the road will be muR where mu is the coefficient of friction and R is the normal reaction between the bike and the road. R will equal the weight of the bike, mg, so friction =mumg

If this is the only force acting on the bike, then by Newton's 2nd law
F=ma
mumg=ma

so dividing both side by m gives:

mug=a=0.7*9.81=6.87ms^-2

We can now use the equation of motion:
v^2=u^2+2as

We know the initial velocity, u=25ms^-1, acceleration a = -6.87ms^-2 (negative since it is decelerating), and v, final velocity is 0ms^-1 (since the bike comes to rest). We want to find the distance, s.

So
0=25^2-2*6.87.s
0=625-13.74*s
s=625/13.74=45.49m

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