Acceleration

Acceleration is the rate of change of velocity. It is calculated by finding the change in velocity and dividing that number by the time taken for the change to occur, as shown in the word equation below;

acceleration = (final velocity – initial velocity) / time taken

This can be written in symbols using either of the following two variations;

a = ( v – u ) / t                        or                            a = ( v₂ – v₁ ) / t

In both cases, a is acceleration and t is time. We then use either v and u to indicate final and initial velocity or we apply subscripts, v₂ and v₁ respectively.

Using SI units, acceleration is measured in metres-per-second-squared (m/s²), velocity is measured in metres-per-second (m/s) and time is measured in seconds (s).

For example, if the velocity of an object had an initial value of 20 m/s and a final value of 30 m/s then the change in velocity would be 10 m/s. And if the time for this change was 2.5 s then the acceleration would be 4 m/s².

Importantly, velocity itself is a combination of speed and direction. If the speed changes then the velocity changes. And, if the direction changes then this too causes the velocity to change – even if the object concerned isn’t speeding up!

Similarly, acceleration is any change in speed so it doesn’t matter whether the object is speeding up or slowing down: in both cases the object is accelerating. To distinguish between these two different cases, we commonly use a positive number for acceleration that is speeding up and a negative number for acceleration that is slowing down.

A key skill for solving acceleration problems is the ability to work with four variables. In many GCSE Physics equations there are only three variables and one mathematical operation (multiplication or division) so the “triangle technique” can be used to rearrange the variables in order to calculate whichever one is unknown. Sadly, things are not quite so easy when dealing with acceleration.

The answer is to convert two of the variables into a combined variable. We do this by taking the change in velocity and giving it a symbol of its own, “delta-v” (Δv). This changes our four-variable equation into a three-variable equation that can be written as follows;

a = Δv / t               where Δv = v₂ – v₁

The simplified format can be handled using the “triangle technique”, with Δv on the top and both a and t on the bottom (in either order, of course).

With this information, you should be able to solve all the numerical questions on the Speed, Velocity and Acceleration worksheet. If you have lost that sheet, you can download a copy by clicking here.

If you need help solving the questions, and you truly have tried as hard as you can, you can download the help sheet (which also contains the answers) here.

Finally, there is a summary explaining the “triangle technique” that you can download here.