How to Interpret Velocity-Time Graphs in IGCSE Physics

Velocity-time graphs appear in almost every IGCSE Physics exam session. This guide covers everything you need to know about reading them, calculating from them, and sketching them.

What the axes represent

• The x-axis shows time (in seconds).
• The y-axis shows velocity (in m/s).

Each point on the graph tells you the velocity of the object at that moment in time.

Reading the graph

Constant velocity: a horizontal line. The object moves at the same speed in the same direction.

Constant acceleration: a straight line sloping upward. The velocity increases at a steady rate.

Constant deceleration: a straight line sloping downward. The velocity decreases at a steady rate.

Increasing acceleration: a curve that gets steeper over time.

Stationary: a horizontal line at velocity = 0.

Gradient = acceleration

The gradient (slope) of a velocity-time graph gives the acceleration:

acceleration = (change in velocity) / (change in time) = (v2 minus v1) / (t2 minus t1)

• Positive gradient = acceleration (speeding up)
• Negative gradient = deceleration (slowing down)
• Zero gradient (horizontal line) = constant velocity (no acceleration)

To calculate the gradient:

1. Pick two points on the line, far apart.
2. Read the velocity and time values for each point.
3. Calculate: gradient = (v2 minus v1) / (t2 minus t1).
4. Include the unit: m/s squared.

Area under the graph = distance

The area between the line and the time axis gives the distance travelled.

For a rectangular section (constant velocity): area = velocity x time.

For a triangular section (uniform acceleration from rest): area = 0.5 x base x height = 0.5 x time x velocity.

For a trapezoidal section (uniform acceleration between two velocities): area = 0.5 x (v1 + v2) x time.

For a curved section: count the squares under the curve. Each square represents a known distance (read the scale to find the value of one square). Count full squares and estimate partial squares.

Below the time axis

If the line goes below the time axis, the velocity is negative. This means the object is moving in the opposite direction. The area below the axis still represents distance, but in the reverse direction.

Common exam questions

1. “Describe the motion of the object between t = 0 and t = 5 s.” State whether it is accelerating, decelerating, or moving at constant velocity. Give the acceleration or velocity value if you can read it from the graph.

2. “Calculate the total distance travelled.” Find the area under the graph for the entire journey. Split it into sections (rectangles, triangles, trapezoids) and add the areas.

3. “Calculate the acceleration between t = 2 s and t = 6 s.” Find the gradient of that section.

4. “Sketch a distance-time graph for the same motion.” The gradient of a distance-time graph equals the velocity. Where velocity is constant, the distance-time graph is a straight line. Where velocity increases, the distance-time graph curves upward (steepening).