physics question deceleration

Question

A car of mass 1.2 x 1012 kg is travelling along a straight horizontal road at a speed of 20 m/s when it brakes sharply then skids. Friction brings the car to rest. If the coefficient of friction between the tires and road is 0.8, calculate:

a. The deceleration

b. The distance travelled by the car before it comes to rest.

Answer 1

a.) We can find the deceleration by applying Newton's 2nd law: F = ma. Here, the force of friction is causing the car to decelerate. We can calculate the force of friction by multiplying the normal force by coefficient of friction: F_f = -mgµ. Setting these two equations equal gives us ma = -mgµ, which we can simplify to a = -gµ = -9.81*0.8 = -7.85 m/s². The minus sign is important here as the car is decelerating instead of accelerating.

b.) We can solve this by using a kinematic equation for 1 dimensional motion: v_f² - v_i² = 2ax. We know that the final velocity will be 0 because the car is stopped. So, x = -v_i²/(2a) = 20²/(2*7.85) = 25.48 m.

Hope this helps!