In July 2014, Car and Driver magazine crowned the 2015 Porsche 918 Spyder as the quickest production car in existence after it blazed from zero to 60 miles per hour in a paltry 2.2 seconds. Although these figures aptly express the performance of the car, they don't offer a true measurement of acceleration. The constant acceleration formula allows you to calculate a single value that describes the change in velocity over time. Although cars rarely accelerate at a uniform rate, the formula's assumption of such produces an average value that can be compared to other known values, such as gravitational acceleration.
Calculating Constant Acceleration
Write the constant acceleration formula, so you have a basis for the calculation. In this formula, "t" represents time, "v0" represents initial velocity and "v1" represents final velocity.
Replace the variables with available data. In the Porsche example, the initial velocity is zero miles per hour and the final velocity is 60 miles per hour during the time-span of 2.2 seconds. It's typically a good idea to keep the units in the equation, because they help identify problem areas, such as different units for velocities. In this example, it's easy to see that the velocity (miles per hour) and time (seconds) use different units of time. That's not a problem however, because you're dividing through to create a new unit--miles per hour, per second. If you prefer to use consistent units, divide the seconds by 3,600 to convert to hours. However, the resulting acceleration would be an enormous number and difficult to compare.
Subtract the initial velocity from the final velocity to calculate the change in velocity due to acceleration. In the example, the initial velocity is zero, so you're left with the final velocity of 60 miles per hour.
Divide the change in velocity by the time to calculate the acceleration in units of velocity per time. In the example, 60 miles per hour divided by 2.2 seconds equals an acceleration of 27 miles per hour, per second. That means that on average, the velocity increases by 27 miles per hour for every second that passes. Note that when writing the units in the equation, "miles per hour, per second" is simplified to "mi / (hr x sec)." If you wonder how this figure stacks up against gravity, you'll need to convert the measurement into the same units used to measure gravity.
To convert the acceleration measurement in the example, multiply miles times 5,280 feet per mile to convert it to units of feet. Likewise, multiply hours times 3,600 seconds per hour to convert it to units of seconds. This converts the original measurement to 40 feet per second, per second or simply 40 feet per second-squared. Compared to gravitational acceleration's 32 feet per second-squared, the Porsche 918 actually accelerates you faster than gravity would accelerate you after jumping out of an airplane.
Other acceleration-reducing factors, such as wind drag, become more important as velocity increases. This means the constant acceleration assumption isn't valid, but this doesn't affect the accuracy of the average. However, if you're looking for exact measurements of performance during a specific time-period, it's better to use small windows of time that more accurately represent the target stage. As an example, measuring acceleration in the first second more accurately describes the initial acceleration, rather than relying on an average during the first 15 seconds.