Question

How much farther will a car skid if it locks its brakes at 60 mph as compared to a skid from 15 mph? Assume the braking force that will eventually stop the cars is provided by the road and that it acts with equal magnitude in both situations. Distance increases by a factor of 4 times 16 times impossible to tell because the mass of the car is not known impossible to tell because frictional force is not known

Answer 1

v₀ = initial velocity of the car before brakes are applied

v = final velocity of the car after it comes to a stop = 0 mph

d = stopping distance

a = acceleration caused due to braking force

Using the kinematics equation

v² = v²₀ - 2 a d

0² =  v²₀ - 2 a d

d = v²₀ /(2a)

Since the acceleration is same , the stopping distance is directly proportional to the square of the initial speed of car before brakes are applied

hence

d₁/d₂ = v²₀₁/v²₀₂

Given that : v₀₁ = 60 mph   and v₀₂ = 15 mph

inserting the values

d₁/d₂ = (60)²/(15)²

d₁ = 16 d₂

hence distance increases by a factor of 16 times.