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
Apr 15, 2016

Answer:

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#