# Calculate the Maximum Acceleration of a Vehicle Given the Maximum Power of its Engine

## Calculation of Maximum Acceleration

Suppose the maximum power delivered by a car's engine results in a force of 16000 N on the car by the road. In the absence of any other forces, what is the maximum acceleration this engine can produce in a 1650-kg car?

**Answer:**

Approximately 9.7 m/s^2.

**Explanation:**

Assuming that there is no other force on this vehicle, the 16000 N force from the road would be the only force on this vehicle. The net force would then be equal to this 16000 N force. The size of the net force would be 16000 N.

Let m denote the mass of this vehicle and let ΣF denote the net force on this vehicle.

By Newton's Second Law of motion, the acceleration of this vehicle would be proportional to the net force on this vehicle. In other words, the acceleration of this vehicle, a, would be:

a = ΣF/m.

For this vehicle, ΣF = 16000 N whereas m = 1650 kg. The acceleration of this vehicle would be:

a = 16000 N / 1650 kg

a = 16000 kg * m * s^-2 / 1650 kg

≈ 9.7 m * s^-2