Acceleration and Velocity Time Graphs

Objectives

Lesson outcomes

Define acceleration as change in velocity per unit time and use the acceleration equation.
Identify constant acceleration, changing acceleration, and deceleration from data or a velocity-time graph.
Calculate acceleration from the gradient of a velocity-time graph.
Use negative values correctly when describing and calculating deceleration.

Syllabus

CIE 0625 syllabus points

4 linked

1.2.9 Define acceleration as change in velocity per unit time; recall and use the equation ∆v a = ∆t
1.2.10 Determine from given data or the shape of a speed–time graph when an object is moving with: (a) constant acceleration (b) changing acceleration
1.2.11 Calculate acceleration from the gradient of a speed–time graph
1.2.12 Know that a deceleration is a negative acceleration and use this in calculations

Definitions

Required definitions

Acceleration
the rate of change of velocity.
Deceleration
negative acceleration that causes velocity to decrease.

Lesson Notes

Student guidance and lesson notes

Overview

This lesson adds the next layer of motion analysis, so the meaning of the graph gradient must stay central. You need to connect three forms of the same idea: the wording of the motion, the numerical calculation, and the shape of the velocity-time graph.

What You Need to Know

Use the definition of acceleration to connect velocity change, time taken, and graph gradient.
Use velocity-time graphs to distinguish constant acceleration from changing acceleration.
Remember that the gradient of a velocity-time graph gives acceleration, not speed.
Keep the deceleration sign convention consistent in calculations.
Compare horizontal, sloping, and curved sections of graphs so you link each shape to the motion described.

How to Work Through It

Start with a retrieval task on velocity and graph gradient from the previous lesson.
Work through the acceleration equation and practise straightforward change-in-velocity calculations.
Interpret several velocity-time graphs, focusing on gradient, sign, and changing slope.
Finish with mixed calculation and graph questions that include deceleration.

Check Your Understanding

Can you explain whether a flat section on a velocity-time graph means zero velocity or zero acceleration, and give a reason.
Use a hinge question where you decide which graph shows constant acceleration and which shows changing acceleration.
Try one graph section and check whether you can calculate the acceleration from its gradient.

Common Mistakes

Reading the height of the graph as acceleration. Revisit that the vertical axis is velocity and the gradient gives acceleration.
Some think deceleration must always be positive because the object is still moving. Keep the sign convention tied to the change in velocity.
Curved sections are often described vaguely. Make you say whether the acceleration is changing rather than just saying the object is “speeding up”.

Next Steps

Set short graph-interpretation practice that includes both positive and negative gradients.
Carry forward the idea of equal time intervals into the ticker-timer lesson.