Kinetic energy and friction Physics Question?

Question

An automobile with passengers has weight 16000 N and is moving at 114 km/h when the driver brakes, sliding to a stop. The frictional force on the wheels from the road has a magnitude of 8230 N. Find the stopping distance.

Answer 1

We are given the weight of the automobile; however a more useful quantity to use (so that we can find the car's Kinetic Energy) would be the car's mass.
Weight = mass * gravity
So we can solve for the mass,
mass = weight / gravity
Plugging in (w = 16000 N, g = 9.81 m/s^2), we get,
mass = 1631 kg

Kinetic Energy (KE) is given as,
KE = 1/2mv^2
Where m is the car's mass, and v is the car's speed.
Before we find its KE, first let’s convert 114 km/h into units of meters per second.
1000 m = 1 km
60 minutes = 1 hour
60 second = 1 minute
114 km/h = 31.7 m/s

Now find KE,
KE = 1/2 (1631 kg) * (31.7 m/s)^2
KE = 819488 Joules


Now, the frictional force is doing work on the car by exerting a force over a distance. The work that the frictional force does goes into changing (lowering) the car's Kinetic Energy.
Work = Force * Distance
We know the force (8230 N) and we know that in order to bring the car to a stop, the Work done must equal the original KE, so W = 819488 J. All we need do now is solve for the distance,
d = Work / Force
d = 819488 Joules / 8230 Newtons
distance = 99.6 meters

So the car will take almost 100 meters (99.6 m) to stop.

Answer 2

A (slightly!) shorter solution:
The deceleration value is (Ff/Fn)*g = (8230/16000)*9.81 = 5.046 m/s²

X = V²/2a = (114000/3600)²/(2*5.046) = 99.36 m

QED