# How to Find the Theoretical 0-60 mph Time of a Car?

• AsifHirai
In summary, the conversation discusses the theoretical 0 to 60 mph time for a car with a weight of 2200 lbs and a peak torque of 750 lb ft at 6500 RPM. The conversation also considers the use of a CVT and racing differential to keep power to all four wheels constant and equal. The solution involves calculating the power output of the engine and the amount of work needed to reach 60 mph, which leads to an estimated time of 16.7 seconds. There is also a discussion about the units used in the calculations and the role of a CVT in optimizing engine performance.
AsifHirai

## Homework Statement

A car weighs 2200 lbs, has a peak torque of 750 lb ft at 6500 RPM. Assume a CVT and racing differential keeps the power to all four wheels of the car constant and equal. What is the theoretical 0 to 60 mph time?

## Homework Equations

$Fd = \frac{1}{2}m v_f ^2 - \frac{1}{2}m v_0 ^2$
$P = \frac{\tau \times \omega}{\Delta t}$

## The Attempt at a Solution

So the power output of the engine is going to be $P = \frac{(750 lb ft)(6500 rpm)(2\pi rad)}{60 sec} = 510,250 \frac{ft lbs}{sec}$
The amount of work needed to get the car up to 60 mph from rest ideally would be $W = \frac{1}{2}(2200 lbs)(\frac{60 mi * 5280 \frac{ft}{mi}}{3600 sec})^2 = 8,518,400 ft lbs$
Dividing those two numbers gives us 16.7 sec. I don't know if my approach is right with the work-energy theorem or if I have to use some other metric for calculating the time because I'm sure it's not that slow if the engine is pushing nearly 1000 hp...

Yeah, you confused the units a little bit. lbs is a unit of force, you have to convert that to a unit of mass for it to work in the work equation (divide by acceleration due to gravity here on Earth).

You can see a problem occurs because your final units in the work equation are lbs*ft^2/s^2 and not lbs*ft

But wouldn't that mean my units for work will be slug ft^2 / s^2? How would I convert that to compare it to the power of the engine?

Wait, slug ft/s^2 = lb, so that would work... thanks

Side note - normally a CVT allows an engine to operate at the rpm for peak power, not peak torque, since with optimal gearing, maximum torque at the real wheels for any given speed (except zero or near zero speeds in a real world situation) corresponds to maximum power from the engine.

## 1. What is the formula for calculating the theoretical 0-60 mph time of a car?

The formula for calculating the theoretical 0-60 mph time of a car is: 0-60 mph time = (weight/horsepower) x (1/5)

## 2. How accurate is the theoretical 0-60 mph time compared to the actual 0-60 mph time?

The theoretical 0-60 mph time is an estimate and may not be completely accurate as it does not take into account external factors such as road conditions, weather, and driver skill. However, it can give a good approximation of a car's performance.

## 3. Can the theoretical 0-60 mph time be used to compare different cars?

Yes, the theoretical 0-60 mph time can be used as a comparison tool between different cars as it provides a standardized measurement of acceleration.

## 4. Is the power-to-weight ratio the only factor that affects a car's 0-60 mph time?

No, there are other factors that can affect a car's 0-60 mph time such as torque, transmission, aerodynamics, and tire grip. However, the power-to-weight ratio is a significant factor in determining a car's acceleration.

## 5. How can I improve my car's theoretical 0-60 mph time?

There are several ways to improve a car's theoretical 0-60 mph time, such as reducing weight, increasing horsepower, improving aerodynamics, and using high-performance tires. However, it is important to note that making modifications to a car can also affect its reliability and longevity.

• Introductory Physics Homework Help
Replies
15
Views
2K
• Engineering and Comp Sci Homework Help
Replies
2
Views
2K
• Engineering and Comp Sci Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
6
Views
1K
• General Engineering
Replies
5
Views
7K
• Mechanical Engineering
Replies
17
Views
4K
• Mechanical Engineering
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
5K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K