Question

A car is travelling along the highway at 90km/h. The driver applies the brakes, the braking action causes a frictional force of 8400 N on the 1050 kg car.
How far does the car travel while it is braking?


Note: answer is 39m but idk how to get there

Answer 1

F = ma
so a = 8400/1050 = -8 m/s^2
90 km/hr = 25 m/s
so
v^2 = 2as
25^2 = 2*8*s
s = 625/16 = 39 m

or, since v = 25-8t, it takes 25/8 seconds to stop, and
s = 25(25/8) - 4(25/8)^2 = 39 m

Answer 2

@oobleck why do we need to multiply v by itself and the acceleration by 2?

Answer 3

BECAUSE
Kinetic energy lost = work done stopping
(1/2) m v^2 = Force * distance = m a * s
so
v^2 = 2 a s

Answer 4

that's what you get if you eliminate t from
v = at
s = 1/2 at^2
note that it also makes the units come out right.