1.2.5Motion, Forces and Energy
Calculating Acceleration from Speed-Time Graphs — Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Revision Notes & Topical Questions
5 min read 8 parts Lesson 8 of 36
Section 1 of 8Shapes of speed-time graphs
| Shape | Meaning |
|---|---|
| Straight line, positive gradient | Constant positive acceleration |
| Curve getting steeper | Acceleration increasing |
| Curve getting shallower | Positive acceleration decreasing |
| Downward curve levelling off | Deceleration decreasing |
Section 2 of 8Constant acceleration
Straight line
- Straight line speed changes by the same amount in equal time intervals
Gradient
- Gradient a = Δv ÷ Δt, where Δv is the change in speed and Δt the change in time
Units
- Units a in m/s², Δv in m/s and Δt in s
Level
- Level this is Extended tier content
Section 3 of 8Changing acceleration
Curve
- Curve the graph is a curve when the acceleration changes
Increasing acceleration
- Increasing acceleration speed changes by the same amount in shorter and shorter times
Decreasing acceleration
- Decreasing acceleration speed changes by the same amount in longer and longer times
Section 4 of 8Acceleration at a point on a curve
Draw a tangent to the curve at the chosen point.
Make the tangent a straight line matching the gradient of the curve at that point.
Draw a large gradient triangle on the tangent.
Calculate gradient
Δy ÷ Δx.
The result is the instantaneous acceleration at that moment.
Section 5 of 8Calculating from a graph
Choose a section
- Choose a section use the entire straight-line section if possible
Draw on the graph
- Draw on the graph show the gradient triangle directly on the graph
Skill
- Skill gradient of a tangent applies to any type of graph
Section 6 of 8More from the specification
1Acceleration from velocity-time slope
- Acceleration from velocity-time slope determining the instantaneous tangent slope on a velocity-versus-time graph yields the instantaneous linear acceleration.
2Gravitational field
- Region where mass experiences gravitational force.
3Field strength
- G = Fg/m.
4Velocity
- Rate of change of displacement.
5Distance
- Total length of path travelled, a scalar.
6Resistance
- Opposition to current, R = V / I, in ohms (Ω).
7Weight
- Gravitational force on a mass.
8Terminal
- Connection point of a cell, labelled + or −.
9Distance-time graph
- Graph of distance against time showing movement.
10Average speed
- Total distance divided by total time.
11Terminal velocity
- Constant speed when air resistance equals weight.
12Slowing acceleration
- Slowing acceleration if acceleration is still positive but getting smaller, the object keeps speeding up, only at a decreasing rate.
Section 7 of 8Key terms
| Term | Meaning |
|---|---|
| Gradient | Δy ÷ Δx of a line. |
| Tangent | Straight line touching a curve at a point. |
| Instantaneous acceleration | Acceleration at one moment. |
| Constant acceleration | Acceleration that does not change. |
| Deceleration | Negative acceleration. |
Section 8 of 8Exam technique
1
Using one point instead of change in speed and time — acceleration needs Δv and Δt.
2
Drawing the tangent in the wrong place — it must touch the curve at the chosen point.
3
Using a small gradient triangle — use a large one for accuracy.
4
Quoting the answer without units — acceleration is in m/s².
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