Question

A car weighing 9800 N travels at 30 m/s. What braking force brings it to rest in 100m? In 10 m?

Answer 1

As per kinematics equation we know that

final speed of the car = 0 m/s

initial speed is given as 30 m/s

distance moved = 100 m

now we have

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

$0 - 30^2 = 2(a)(100)$

$a = - 4.5 m/s^2$

now braking force is given as

$F = ma$

now for mass we know that the weight of car is

$W = mg = 9800 N$

so mass of car is

$m = 1000 kg$

now we have

$F = 1000(4.5) = 4500 N$

Part b)

Again we have

final speed of the car = 0 m/s

initial speed is given as 30 m/s

distance moved = 10 m

now we have

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

$0 - 30^2 = 2(a)(10)$

$a = - 45 m/s^2$

now braking force is given as

$F = ma$

mass of car is

$m = 1000 kg$

now we have

$F = 1000(45) = 45000 N$