3 In reality

The previous section assumes acceleration is constant. That, unfortunately, is not true. Given the same amount of power, acceleration decreases as velocity increases! We can understand this from the point of view of kinetic energy. Kinetic energy is $E=\frac{mv^2}{2}$. You can see that $E$ increases quicker than $v$ because of the square function. This also means that an object gains kinetic energy faster than it gains speed. An object has 4 times the energy when its velocity is doubled.

How about the torque specification? We figured that we need 491 pound-foot at each wheel. However, this is based on the assumption of constant acceleration. Furthermore, car specification usually measures torque at the crank shaft. As if things are not sufficiently complex, there is the transmission and differential between engine shaft and wheels.

Let us think for a moment. The specification mentions 114 pound-foot at 5500rpm. This translates to 153.9Nm. In first gear, the transmission has a ratio of 3.136:1. The differential has an additional 4.1:1 reduction. Combined, there is a 12.86:1 reduction. Torque increases proportionally as gear ratio increases. As a result, in first gear, at 5500rpm, there is a total of 1979Nm at the wheels. This translates to 6754N. At that instant, the acceleration is $6.754ms^{-2}$.