Question

A racing car whose mass is 1.2 X 10^3 kg is travelling at 8.9 m/s. It stops with a constant deceleration in a distance of 1.8X10^1 m. What force must the brakes apply to the car if the friction in the car’s engine is 1.8 X 10^3 N.

Answer 1

given that initial speed of the car is

$v_i = 8.9 m/s$

now after travelling the distance d = 1.8 * 10^1 m the car will stop

so here we can use kinematics to find the acceleration of car

$v_f^2 - v_i^2 = 2 a d$

$0 - 8.9^2 = 2 a d$

here we have

$- 79.21 = 2*(18)*a$

$a = -2.2 m/s^2$

net force applied due to brakes of car is given by Newton's II law

$F = ma$

here we have

mass = 1.2 * 10^3 kg

$F_{net} = 1.2 * 10^3 * 2.2$

$F_{net} = 2.64 * 10^3 N$

now we can say

$F_{net} = F_1 + F_2$

$2.64 * 10^3 = 1.8 * 10^3 + F_2$

$F_2 = 8.4 * 10^2 N$

So the force applied due to brakes is given as above