Estimate the terminal sped of a typical car

shayan ganji

shayan ganji

Answered question


Estimate the terminal sped of a typical car having an engine with a constant power in a flat road, by using the concept of drag force.

Answer & Explanation



Skilled2023-04-24Added 333 answers

To estimate the terminal speed of a car with a constant power engine on a flat road, we can use the concept of drag force.

The drag force on a car is given by the equation:


Fd is the drag force in N (Newton)
ρ is the air density in kg/m^3 (kilograms per cubic meter)
- v is the velocity of the car in m/s (meters per second)
Cd is the drag coefficient, which depends on the shape of the car and its orientation relative to the airflow
- A is the frontal area of the car in m2 (square meters)

The drag force is opposed by the force of the car's engine, which is given by:

Fengine is the force of the car's engine in N
Pengine is the power of the engine in W (Watts)

At the terminal speed of the car, the drag force and the force of the engine are equal and opposite. Therefore, we can set Fd=Fengine and solve for the velocity v:
12ρv2CdA=Pengine v

Simplifying the equation, we get:

Taking the cube root of both sides, we get:

So, the terminal speed of the car can be estimated using this equation, given the air density, the drag coefficient, the frontal area, and the power of the car's engine.

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