Acceleration: Using the Equation (Worked Examples)

Explained

Working with the acceleration equation

Acceleration is the change in velocity divided by the time taken. Written out, that is a equals v minus u over t, where u is the initial velocity and v is the final velocity. The unit is metres per second squared.

The change in velocity is always the final value minus the initial value, in that order. Getting them the wrong way round is the single most common mistake in this topic, and it is what produces a positive answer where a negative one was expected.

What a negative answer means

If the object is slowing down, v is smaller than u, so the top of the fraction is negative and the acceleration comes out negative. That is deceleration, and it is not an error.

Some questions ask for the deceleration rather than the acceleration. In that case give the size of the number without the minus sign, because the word deceleration already carries the direction.

Rearranging it

Three quantities can be asked for, so the equation appears in three forms.

• To find acceleration, divide the change in velocity by the time.
• To find the change in velocity, multiply the acceleration by the time. Then add u to get the final velocity, or subtract from v to get the initial velocity.
• To find the time, divide the change in velocity by the acceleration.

Rather than memorising three versions, put the numbers you have into the original equation first and then solve for the letter that is left. A rearrangement done in advance cannot be checked; a substitution can.

A worked example

A car speeds up from 8 m/s to 20 m/s in 4 seconds. The change in velocity is 20 minus 8, which is 12 m/s. Divide by 4 seconds and the acceleration is 3 m/s squared.

Now the same car brakes from 20 m/s to rest in 5 seconds. The change is 0 minus 20, which is minus 20 m/s. Divide by 5 and the acceleration is minus 4 m/s squared, or a deceleration of 4 m/s squared.

The second equation

When the time is not given but the distance is, use v squared equals u squared plus two a s, where s is the distance travelled. This one is provided in the paper, so the skill being tested is choosing it and substituting correctly rather than recalling it.

Recognising which equation to use comes down to reading what the question gives you. If you have a time, use the first. If you have a distance and no time, use the second.

Two habits that protect marks

Convert to SI units before you calculate. A speed given in kilometres per hour or a distance in centimetres will not produce an answer in the right unit otherwise.

Show every step of the working. Where a final answer is wrong, clear working can still earn method marks, and where nothing is written down there is nothing to credit.