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

A motorcycle moving at 25.0ms 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
Apr 15, 2016

Minimum stopping distance = 45.49m

Explanation:

The friction between the bike and the road will be μR where μ 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 =μmg

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

so dividing both side by m gives:

μg=a=0.79.81=6.87ms2

We can now use the equation of motion:
v2=u2+2as

We know the initial velocity, u=25ms1, acceleration a=6.87ms2 (negative since it is decelerating), and v, final velocity is 0ms1 (since the bike comes to rest). We want to find the distance, s.

So
0=25226.87.s
0=62513.74s
s=62513.74=45.49m