Calculate acceleration from the gradient of a speed-time graph

What is Acceleration?

Acceleration is the rate at which an object's speed changes over time. If you’re riding a bike and you press the pedal harder, your speed increases – that increase is acceleration.

Mathematically, acceleration is defined as the change in velocity divided by the change in time:

$$a = \frac{\Delta v}{\Delta t}$$

Here, $\Delta v$ is the change in speed (final speed – initial speed) and $\Delta t$ is the time interval over which that change occurs.

Speed‑Time Graphs: The Gradient is the Acceleration

On a speed‑time graph, the gradient (slope) of a straight line segment tells you the acceleration. Think of it like a hill: the steeper the hill, the faster you’re speeding up.

For a straight line segment:

$$\text{Gradient} = \frac{\text{Rise}}{\text{Run}} = \frac{\Delta v}{\Delta t} = a$$

So, to find acceleration, simply calculate the slope of the line segment on the graph.

Step‑by‑Step Example

Suppose a car’s speed-time graph shows:

1. Identify two points on the straight line segment: (0 s, 0 m/s) and (5 s, 20 m/s).
2. Calculate the change in speed: $\Delta v = 20 - 0 = 20\ \text{m/s}$.
3. Calculate the change in time: $\Delta t = 5 - 0 = 5\ \text{s}$.
4. Compute the gradient (acceleration):
• $a = \dfrac{\Delta v}{\Delta t} = \dfrac{20}{5} = 4\ \text{m/s}^2$

?? The car’s acceleration is 4 m/s².

Exam Tips for IGCSE Physics 0625

• 📌 Read the question carefully. It may ask for the gradient of a specific segment or the overall acceleration.
• 📌 Show your work. Write the formula $a = \frac{\Delta v}{\Delta t}$ and plug in the numbers.
• 📌 Units matter. Keep track of m/s and s to get m/s².
• 📌 Check the graph. If the line is not straight, you’ll need to pick two points on the same segment.
• 📌 Use a calculator if needed. But for simple numbers, mental math works fine.

Quick Quiz

On a speed‑time graph, a straight line runs from (2 s, 10 m/s) to (8 s, 40 m/s). What is the acceleration?

1. Δv = 40 m/s – 10 m/s = 30 m/s
2. Δt = 8 s – 2 s = 6 s
3. Acceleration = 30 m/s ÷ 6 s = 5 m/s²

Great job! 🎉 Keep practicing and you’ll ace the IGCSE physics exam.