Acceleration and Motion Graphs: Quick Revision

A brief note on Acceleration and Motion Graphs. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Acceleration $a = \dfrac{v - u}{t}$, in $\text{m/s}^2$: how quickly the velocity changes.
• Speeding up: $a > 0$. Slowing down (retardation): $a < 0$, when moving in the positive direction.
• Distance-time graph: flat means at rest, straight means steady speed, the slope is the speed.
• Velocity-time graph: the slope is the acceleration, and the area under the line is the distance.

The facts at a glance

A worked example

A lift's speed is read every second: $0, 1.5, 3, 3, 3, 1.5, 0\ \text{m/s}$. Find its acceleration in each part and how far it rises.

1. Starting. $+1.5\ \text{m/s}^2$ for $2\ \text{s}$.
2. Middle. $0\ \text{m/s}^2$ for $2\ \text{s}$. Stopping. $-1.5\ \text{m/s}^2$ for $2\ \text{s}$.
3. Height. Triangle $\tfrac12 \times 2\ \text{s} \times 3\ \text{m/s} = 3\ \text{m}$, rectangle $2\ \text{s} \times 3\ \text{m/s} = 6\ \text{m}$, triangle $3\ \text{m}$: $12\ \text{m}$ in all.

Practice with new numbers

A program to try

The program works out the lift.

Mistakes to avoid

• Mixing the two graphs. Read the axis label before you read the shape.
• 'Negative slope means slowing down'. On a position graph it means moving back.
• 'Zero velocity means zero acceleration'. Not at the top of a throw.
• Rectangles for triangles. The area under a sloping line from zero is half the rectangle.
• km/h in $a = \dfrac{v - u}{t}$. Change to m/s first.

Check yourself

1. A car goes from $5\ \text{m/s}$ to $17\ \text{m/s}$ in $4\ \text{s}$. What is its acceleration?

2. What does a flat line on a velocity-time graph mean?

3. On a distance-time graph, line X is steeper than line Y. Which object is faster?

4. A velocity-time graph is a flat line at $9\ \text{m/s}$ for $6\ \text{s}$. How far does the object go?

5. A train slows from $20\ \text{m/s}$ to $8\ \text{m/s}$ in $24\ \text{s}$. What is its acceleration?