Lesson summary
2.1.2 Motion Graphs — AS PHYSICS 9702 notes: Interpret distance-time, displacement-time, speed-time, velocity-time and acceleration-time graphs.Distance-time — the slope is speed.Displacement-time — the slope is velocity.Speed-time — the slope is acceleration and the area is dist…
- A straight diagonal line
- The slope is never negative
- A positive slope means motion in the positive direction
- A peak on the graph
- A straight line means uniform acceleration
- A positive slope means speed is increasing
Section 1 of 11Five types of motion graph
Five types of motion graph
Distance-time
- Distance-time the slope is speed.
Displacement-time
- Displacement-time the slope is velocity.
Speed-time
- Speed-time the slope is acceleration and the area is distance.
Velocity-time
- Velocity-time the slope is acceleration and the area is displacement.
Acceleration-time
- Acceleration-time the area is the change in velocity.
Section 2 of 11Distance-time graphs
Distance-time graphs
Slope equals speed.
The y-intercept equals the initial position.
A straight diagonal line
- A straight diagonal line constant speed, a curved line is acceleration and a horizontal line is rest.
The slope is never negative
- The slope is never negative because distance is a scalar.
The area under the curve is meaningless.
Section 3 of 11Displacement-time graphs
1
Slope equals velocity.
2
The y-intercept equals the initial position.
3A straight diagonal line
- A straight diagonal line constant velocity, a curved line is acceleration and a horizontal line is rest.
4A positive slope means motion in the positive direction
- A positive slope means motion in the positive direction and a negative slope means motion in the negative direction.
5A peak on the graph
- A peak on the graph means the object turned round; at the top of a thrown ball's graph the gradient is zero.
6
The area under the curve is meaningless.
Section 4 of 11Speed-time graphs
Speed-time graphs
Slope equals acceleration.
The y-intercept equals the initial speed.
A straight line means uniform acceleration
- A straight line means uniform acceleration a curved line means non-uniform acceleration.
A positive slope means speed is increasing
- A positive slope means speed is increasing a negative slope means speed is decreasing;
- a horizontal line means constant speed.
The area under the curve equals the distance travelled.
Section 5 of 11Velocity-time graphs
1
Slope equals acceleration.
2
The y-intercept equals the initial velocity.
3A straight line means uniform acceleration
- A straight line means uniform acceleration a curved line means non-uniform acceleration;
- a horizontal line means constant velocity.
4A positive slope means velocity is increasing in the positive direction
- A positive slope means velocity is increasing in the positive direction a negative slope means velocity is increasing in the negative direction.
5A line crossing the time axis
- A line crossing the time axis means the velocity changes sign, so the object reverses direction.
6
The area under the curve equals the displacement.
Section 6 of 11Acceleration-time graphs
The slope is meaningless.
The y-intercept equals the initial acceleration.
A horizontal line
- A horizontal line constant acceleration, and a blank graph (a line at zero) means constant velocity.
A straight diagonal line
- A straight diagonal line increasing acceleration.
The area under the curve equals the change in velocity.
Section 7 of 11Linking the graphs
Linking the graphs
Slope of the displacement-time graph gives velocity
- Slope of the displacement-time graph gives velocity slope of the velocity-time graph gives acceleration.
Area under the acceleration-time graph gives Δv
- Area under the acceleration-time graph gives Δv area under the velocity-time graph gives Δs.
Gradient converts a graph to the next lower one
- Gradient converts a graph to the next lower one and area converts it to the next higher one.
At every join between sections the values must match
- At every join between sections the values must match velocity and displacement cannot jump instantly.
A lift that accelerates up, cruises and stops has a v-t graph that rises, stays level and falls.
- Its a-t graph is a positive step, a zero section and a negative step of equal area.
Section 8 of 11Reading and drawing graphs accurately
1Check the axes first
- Check the axes first distance-time and displacement-time graphs, and speed-time and velocity-time graphs, differ subtly.
2Gradient on a straight section
- Gradient on a straight section use a large triangle and show the values taken.
3Gradient on a curve
- Gradient on a curve draw a tangent that touches the curve at one point only.
4Unit of a gradient
- Unit of a gradient the unit of the y-axis divided by the unit of the x-axis.
5Label both axes with quantity and unit
- Label both axes with quantity and unit and mark key values.
Section 9 of 11More from the specification
1Kinematic Equations for Uniform Acceleration
- For motion in a straight line under constant gravitational acceleration g, kinematic equations link initial velocity u, final velocity v, acceleration a, time t,
- and displacement s.
- (e.g. v² = u² + 2as and s = ut + ½at²)
2Determining g with a Ball-Bearing Experiment
- In an experiment to measure acceleration of free fall, an electromagnet releases a ball-bearing from a measured height h through light gates,
- and kinematic equations are applied to the average time taken (h = ½gt²).
3Projectile Motion and Graph Interpretation
- In projectile motion, horizontal velocity remains constant while vertical velocity represents uniform acceleration;
- on a vertical velocity-time graph, the gradient represents gravitational acceleration g.
4Projectile
- Object moving under gravity alone in two dimensions.
5Electromagnet
- Magnet made by current through a coil around a magnetic core.
6Kinematic equations
- Equations relating displacement, velocity, acceleration and time for constant acceleration.
7Final velocity
- Velocity at the end, v.
8Projectile motion
- Two-dimensional motion with constant horizontal velocity and vertical acceleration g.
9Vector quantity
- A quantity with both magnitude and direction.
10Light gate
- A sensor that starts or stops a timer when a beam is interrupted.
Section 10 of 11Key terms
| Term | Meaning |
|---|---|
| Gradient | Change in the y-quantity divided by the change in the x-quantity. |
| Tangent | A straight line touching a curve at one point whose gradient is the rate of change there. |
| Area under a graph | The accumulated quantity, for example displacement under a v-t graph. |
| Displacement-time graph | A graph of displacement against time whose gradient is velocity. |
| Velocity-time graph | A graph of velocity against time whose gradient is acceleration and area is displacement. |
| Speed-time graph | A graph of speed against time whose area is distance. |
| Acceleration-time graph | A graph of acceleration against time whose area is the change in velocity. |
| Uniform acceleration | Acceleration shown by a straight sloping line on a velocity-time graph. |
Section 11 of 11Exam technique
1
Reading the height of an s-t graph as speed — speed is the gradient.
2
Treating a v-t graph as the path of the object — it shows how velocity changes.
3
Saying a horizontal line on a v-t graph means rest — it means constant velocity, rest only if v = 0.
4
Confusing distance-time with displacement-time graphs — only displacement-time graphs can have negative gradients.
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).