# Stopping a car before collision

1. Jan 17, 2014

### hav0c

1. The problem statement, all variables and given/known data

A person driving a car suddenly sees a wall .At that instant velocity of the car is v. Coefficient of static and kinetic friction is μ. The mass of the car is M. To avoid the driver should ....(acc. due to gravity=g)
a)apply breaks
b)turn (the car shouldn't slip while turning)
c)apply breaks while turning (the car wont topple)

2. Relevant equations
v=rω
f=ma
v=d(s)/d(t)
... other equations of motion
(ignore actual scenario of pumping the brakes)

3. The attempt at a solution
In case the driver applies the brakes the distance travelled is simply (v2)/(2μg).
In case the driver turns the radius of the turn will be (v2)/(μg))
How will i work out the case of applying breaks and turning ?

2. Jan 17, 2014

### lightgrav

Keeping maximum Force magnitude applied at some (fixed) angle from -v ...
you know the result for 0° is half the result for 90°.
Suppose you try it at 45° (then a∙r=-v∙v makes r become a function of remaining KE ... too bad).
The Force component pointing away from the wall is 71%, weaker than the simple braking case (100%),
so the Work done by that component while traveling to the wall must be less, at any other angle.
This means that the forward component of velocity is changed less, if F applied at any non-180 angle.