Acceleration changes velocity

How to notice an acceleration

So you can notice an acceleration, and the lurches of acceleration we've introduced. Examples we've picked so far might suggest the following effects of an acceleration:

• You're noticed to slow down.
• You're noticed to speed up.
• You're noticed to be moving in a new direction.

Take a moment to match these to the following examples:

1. A plane taking off.
2. A plane landing.
3. A braking car.
4. A car pulling away from traffic lights.
5. A car cornering.
6. A kayak pitching in a rough sea.

You might also find it useful to match the three categories (speeding up, slowing down and changing direction) to examples of your own.

You can draw together all of these seemingly disparate statements into a single statement:

acceleration changes velocity.

That's quite some claim, and a significant synthesis, so we'll spend some time exploring the idea.

Thinking with units

We hope you managed to do the matching well, and to add your own examples to our list:

• 2, 3
• 1, 4
• 5, 6

We've already met acceleration, in episode 1, as a consequence of force acting on mass. There it had the units of (metre/second) every second. Lots of physical quantities have units like this, and so can be thought of as instructions to accumulate. Here are two more: Energy, power and time: Δ energy = power × time interval (expressed using units, this is joule = joule second^-1 × second). Number, activity and time: Δ number = activity × time interval (expressed using units, this is no units = second^-1 × second). (Remember: Δ x is just shorthand for change in x.)

Acceleration and velocity follow this pattern: Δ velocity = acceleration × time interval (expressed using units, this is metre second^-1 = metre second^-2 × second. In this topic this pattern of accumulation is particularly important. This is the first of many meetings.

We'll get to look at velocity in more detail in this episode. For now, it's simply the result of accumulating acceleration.

Understanding acceleration as an accumulation

Acceleration is all about driving an accumulation.

For every second that the acceleration occurs, the velocity changes by a set amount. This change could be positive or negative, so the acceleration could be positive or negative.

A constant positive acceleration adds a fixed number of metres/second to the velocity in each second.

A constant negative acceleration subtracts a fixed number of metres/second from the velocity in each second.

Usually you'll stick to one-dimensional motion. The magnitude of the increment or decrement is fixed by the magnitude of the acceleration. Whether it's an increment or decrement is fixed by the direction, shown by a sign in the simple one-dimensional case.

However, do remember that acceleration is a vector, with all that this implies about changing velocity in two and three dimensional cases.