1.2 Acceleration

Measurements of rate don’t stop with speed and velocity. Acceleration is the rate of change of velocity (or speed, but physicists tend to prefer velocity—it’s more descriptive). So average acceleration is the rate of change of the rate of displacement, the standard units for which are "meters per second per second", or "meters per second squared" (m/s2). Mathematically, this translates to:

For those with some calculus experience, acceleration is the first derivative of velocity (which is the first derivative of position). But don’t worry, even if you haven’t studied calculus yet, you can still understand a lot about velocity and acceleration.

Take, for example, a car traveling at 60 kilometers per hour (km/h). The driver decides to enter the freeway, where the speed limit (although, since direction of travel is relevant, perhaps it should be called the "velocity limit") is 100 km/h. The car must accelerate to avoid an accident. In 5.0 seconds, the driver accelerates at a constant rate from 60 km/h to 100 km/h. What was the car’s average acceleration? Average acceleration is the quotient of change in velocity and time elapsed, so:

Since we will be dividing by seconds, km/h can be converted to m/s for ease.