Calculating Acceleration Using Change in Velocity

When objects speed up, we say they are accelerating.
When they slow down, they are decelerating.
In physics, both of these situations are described using the idea of
acceleration.

Acceleration is defined as the change in velocity divided by the
time taken. This relationship allows us to calculate acceleration
(or deceleration) in a wide range of GCSE Physics problems.

The Acceleration Equation

Acceleration can be calculated using the formula:

a = Δv / t

Here, the symbol Δ (delta) means change.
Velocity is a vector, so direction matters — a change in direction
also counts as a change in velocity.

• a — acceleration (m/s²)
• Δv — change in velocity (m/s)
• t — time taken (s)

The change in velocity can also be written as:

Δv = v − u

where v is the final velocity and
u is the initial velocity.

Understanding the Units of Acceleration

Acceleration is measured in m/s². This means the velocity changes
by a certain number of metres per second every second.

For example, an acceleration of 3 m/s² means the velocity increases
by 3 m/s each second. Starting from rest, the object would have speeds of
3 m/s after 1 second, 6 m/s after 2 seconds, and 9 m/s after 3 seconds.

Worked Example: Braking Car

Consider a car travelling at 15 m/s that begins to brake with a
deceleration of 2 m/s². Since the car is slowing down,
the acceleration is written as −2 m/s².

The car comes to rest, so its final velocity is 0 m/s.
The change in velocity is therefore:

Δv = 0 − 15 = −15 m/s

Substituting into the equation:

−2 = −15 / t

Rearranging gives:

t = 7.5 s

This means the car takes 7.5 seconds to come to rest.

In summary: acceleration is the rate of change of velocity.
A negative acceleration simply indicates deceleration, and careful use
of signs and units is essential for full marks in GCSE Physics calculations.