Motion problem...?

Question

When traveling at 100 km/h a car has to overcome a drag force due to air resistance of 800 N. If the car has a mass of 900kg determine the average force that the motor needs to apply if it is to accelerate at 2.ms^-2.

This confuses me greatly. Its a textbook question and the answer is 2600 N. Any help showing steps or explaining how this works is appreciated :)

thanks.

Answer 1

m = 900kg

a = 2m/s²

D = 800N ........ the drag force

F = ? ........the force of the motor

ma = sum of the forces on the car

ma = F - D

F = ma + D = 900*2 + 800 = 2600N

.,.,

Answer 2

Consider direction in which car is accelerated as positive.

Mass m = 900 kg

Acceleration a = 2 m/s^2

Drag force Fd = -800 N (negative because drag force opposes motion)

Force by motor Fm = ?

Total force F = ma

Again, F = Fd + Fm

Therefore, Fd + Fm = ma

Or, -800 + Fm = 900 * 2

Or, Fm - 800 = 1800

Or, Fm = 1800 + 800 = 2600 N

Ans: 2600 N