Question

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`.

Answer 1

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`