Velocity can change: you can speed up or slow down, or start going in a different direction. The process of changing velocity is called acceleration. The quantitative definition of acceleration is

Acceleration = (final velocity - initial velocity)/ (elapsed time)

Please note that it is the change in velocity that matters; you can be going fast and not accelerating, and you also can be accelerating while not going very fast. Acceleration has a direction as well as a size, just like velocity. If you change direction of motion, this is a change in velocity; thus you can accelerate with changing your speed at all, by changing direction of motion.

Since velocity is measured in units of meters per second, acceleration is measured in units of "meters per second per second" because we divide by time to calculate it. This can also be written "m/sec²"

Here are some examples:

• In the activity Rolling Downhill the velocity of the ball changed. The initial velocity was zero; let's assume the final velocity is 0.6 m/sec to the right. If it took 2 seconds to accomplish this change, the acceleration is
     acceleration = (0.6 m/sec to the right - 0 m/sec)/2 sec = 0.3 m/sec² to the right
  The acceleration is in the same direction as the velocity, because the ball is speeding up. If the ball were slowing down, the acceleration would be in the opposite direction.
• As a car moves away from a stop sign, its forward speed is increasing. Its initial velocity is zero, and so the car is accelerating forwards. If it changes speed in a short time, the acceleration is large. We can calculate the acceleration of the car for any part of its trip. For example, if the car changes its velocity from 10 m/sec to 15 m/sec in 10 seconds, the acceleration is
    acceleration = (15 m/sec - 10 m/sec)/10 sec = 0.5 m/sec²

• As a car arrives at a stop light, its forward speed is decreasing. When you calculate the acceleration, you get a negative number for the forward acceleration; or we could say that the car is accelerating backwards.
• A falling (or thrown) object is an interesting special case. The acceleration is constant: it is 9.8 m/sec² downwards (for objects on Earth). Suppose you drop a coin, which falls to the floor in 0.6 seconds. Here is how to calculate its speed just before it hits the floor:
    acceleration = 9.8 m/sec² downward = (final velocity - initial velocity)/0.6 sec
  The initial velocity is zero (if you just drop it); then
    final velocity = 9.8 m/sec² x 0.6 sec = 5.9 m/sec -- about 13 mph

We have a lot of experience with acceleration, from dropping things. Unfortunately, the acceleration of a falling object is too large for us to be able to study it with meter sticks and stopwatches, In 1 second a ball will fall 5 m (16 feet), which won't fit in a classroom. Any ball-dropping experiment you can do in the classroom would be over in less than a second, which will be difficult to time accurately with a stopwatch (for example, a ball will fall 1 meter (3 feet) in 0.45 second). However, a ball rolling on a slightly inclined track accelerates much more slowly.

In the activity Rolling Downhill we did not determine the final speed of the ball -- we only calculated the average speed. The final speed will be greater than this. This means that we cannot calculate the acceleration correctly. However, the activity does show that the average velocity increases in proportion to the time on the ramp, which implies that the acceleration is constant.