Question

What's the largest acceleration a car can have if uk=0.38 and us= 0.65? please show work

Answer 1

Maximum acceleration will be obtained at the instant immediately before the tyre starts to move;

(Take an example of bike, when you start your bike you accelerate more to overcome static friction between the tyres and road after that bike need less acceleration to overcome kinetic friction.)

now,

Using Newton's 2nd Law of Motion;
F = ma;

and this force is equal to frictional force;

therefore;

(coefficient of static friction) *mg = ma;

a = (coefficient of static friction)*g;

= 0.65*9.8;

= 6.37 m/s²