Question

An automobile has a mass of 1200 kg. what is its kinetic energy, in kj, relative to the road when traveling at a velocity of 50 km/h? if the vehicle accelerates to 100 km/h, what is the change in kinetic energy, in kj?

Answer 1

One thing you should notice. It is kind of weird. Ke has no direction so that fact that it has velocities associated with it does not matter. It becomes a scaler (something measured by amount alone).

General Formula
Ke = 1/2 m v^2
Formula for this problem
Ke = 1/2 m (v2)^2 - 1/2 m (v1)^2

Givens
m = 1200 kg
v2 = 100 km/hr = 100 km/h * [1 hour / 3600 sec] * [1000 m/ 1km] = 27.8 m/s
v1 = 50 km / hr = 13.9 m/s

Substitution and work.
================
delta Ke = 1/2 1200 (27.8)^2 - 1/2 1200 (13.9)^2
delta Ke = 463704 - 115926
delta Ke = 34778 Joules
delta Ke = 34.8 kJ

The change is 34.8 kJ which means that the vehicle gains 34.8 kJ