a 1000kg car moving north @ 100 Km/h brakes to a stop in 50m. What are the magnitude and direction of the force?

beginning velocity (V0)= 100 Km/h
ending velocity (Vf)= 0
distance = 50 m
mass= 1000 Kg

To find the force, you'll need to calculate the acceleration, then use f=ma to solve for the force.

To find the acceleration, you could simply solve



However, you don't know the time t. To find the time, you could use



You know (the distance traveled while the car was braking, 50m), and it's easy enough to calculate . The car started at 100 km/h, and ended at 0 km/h, so its average velocity was 50 km/h.

The only remaining step is to convert the time from hours to seconds so that the force comes out in Newtons.

As for the direction of the force, what does your intuition say? What direction would you have to push on the north-traveling car in order to make it come to a stop? The answer should also appear out of the math, because the above equations are set up as if the acceleration a is in the same direction as the car is traveling (north). Hence, if the force you calculate comes out to be positive, that means it's directed toward the north. However, if it comes out negative, that means it's the same as a positive force directed toward the South.

One of my favourite kinematics equations...



where v is the final velocity,
u is the initial velocity,
a is the acceleration,
s is the displacement.

You can find a, then use F = ma to get the force of braking.

Note that you need to use consistent units! Km/h for example should first be converted to m/s if you use my formula, or else, you will miss the answer.