# Calculating Max Velocity of 2 Tonne Car: 60kW Power

• Bucky
In summary, to determine the maximum velocity of a car with a mass of 2 tonnes and an engine generating 60kW of power on a level road with a coefficient of friction of 1/2, we can use the equation v = P/\mu_kmg, where v is the maximum velocity, P is the power of the engine, \mu_k is the kinetic coefficient of friction, m is the mass of the vehicle, and g is the gravitational acceleration. This equation tells us that the maximum velocity is reached when the force of the car's tires pushing against the road is equal to the force of the road pushing back, at which point the car will stop accelerating. Therefore, the maximum velocity is dependent on the power of
Bucky
"A car of mass 2 tonnes has an engine that can generate 60kW of power. Determine its maximum velocity in m/s along a level road that has a coefficient of friction 1/2"

well I am quite lost. i know:-

power is force times velocity...and force is mass times acceleration...but I am not sure how to apply these.

since its the maximum velocity the force applied would 'cancel out' the force of the friction so there would be no increase in speed.

but to be honest I am really not sure where to go from here.

The friction force is independent of the force applied. You can find the magnitude of the friction force with the given information.

After that, I don't know though.

I suppose that's the kinetic coefficient of friction... in that case, we know that the kinetic frictional force will be:

$$F = \mu_k N$$, where mu is the kinetic coefficient of friction and N is the normal force (the mass of the vehicle times gravitational acceleration).

Now, we know something stops accelerating when the forces on it add up to zero... so it will be a matter of saying that the maximum velocity has been reached when the car's tires are pushing ahead as much as the road is pushing back.

$$F_f = \mu_k N$$

$$F_c = P/v$$

$$F_f = F_c$$ (at max velocity)

$$v = P/\mu_kmg$$

In SI units, remember.

## 1. How do you calculate the maximum velocity of a 2 tonne car using 60kW power?

The maximum velocity of a car can be calculated using the formula: Velocity = (Power x 1000) / (Mass x 0.5 x Drag Coefficient x Frontal Area x Air Density). In this case, the power is given as 60kW and the mass is 2 tonnes (2000 kg). The drag coefficient, frontal area, and air density can be found by researching the specific make and model of the car. Once these values are known, the velocity can be calculated.

## 2. Can the maximum velocity of a car be limited by its power?

Yes, the maximum velocity of a car is directly affected by its power. A more powerful car will have a higher maximum velocity compared to a less powerful car, all other factors being equal.

## 3. What is the significance of the car's mass in calculating its maximum velocity?

The mass of a car plays a significant role in determining its maximum velocity. A heavier car will require more power to overcome its inertia and reach a certain velocity. This means that a 2 tonne car will have a lower maximum velocity compared to a 1 tonne car with the same power output.

## 4. How does the drag coefficient and frontal area affect the maximum velocity of a car?

The drag coefficient and frontal area of a car determine how aerodynamic it is. A car with a lower drag coefficient and smaller frontal area will require less power to reach a certain velocity compared to a car with a higher drag coefficient and larger frontal area. This means that a car with a more streamlined design will have a higher maximum velocity compared to a car with a less aerodynamic design.

## 5. Is air density a significant factor in calculating the maximum velocity of a car?

Yes, air density plays a significant role in determining the maximum velocity of a car. Air density is affected by factors such as altitude, temperature, and humidity, and it can greatly impact the amount of resistance the car experiences as it moves through the air. A higher air density will result in more resistance and therefore a lower maximum velocity, while a lower air density will result in less resistance and a higher maximum velocity.

• Introductory Physics Homework Help
Replies
57
Views
822
• Introductory Physics Homework Help
Replies
2
Views
908
• Introductory Physics Homework Help
Replies
19
Views
1K
• Introductory Physics Homework Help
Replies
29
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
831
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
18
Views
2K
• Introductory Physics Homework Help
Replies
21
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
29
Views
2K