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?

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

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