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 Motion – Understanding Acceleration

What is Acceleration?

Acceleration is the rate at which an object’s speed changes.

Mathematically it is written as \$a = \dfrac{\Delta v}{\Delta t}\$.

If \$a\$ is the same at all times, the object has constant acceleration.

If \$a\$ changes, the acceleration is changing.

Speed‑Time Graphs

On a speed‑time graph the slope of the line equals the acceleration:

\$a = \dfrac{\text{slope}}{1}\$.

- A straight line with a constant positive slope → constant positive acceleration.

- A straight line with a constant negative slope → constant negative acceleration (deceleration).

- A curved line → acceleration is changing (increasing or decreasing).

Examples with Data Tables

Time (s)Speed (m/s)
00
210
420
630
840

This table shows a straight line on a speed‑time graph → constant acceleration of \$a = 5\,\text{m/s}^2\$.

Time (s)Speed (m/s)
00
210
425
645
870

Here the slope increases with time → acceleration is changing (increasing).

Think of a roller‑coaster that speeds up as it goes down the hill 🎢.

How to Spot Constant Acceleration on a Graph

  • Check if the line is straight (no curves).

  • All segments of the line have the same slope.

  • Equal time intervals give equal changes in speed.

  • Example: from 0 s to 2 s speed increases by 10 m/s, from 2 s to 4 s also 10 m/s.

How to Spot Changing Acceleration on a Graph

  • The line is curved or has segments with different slopes.

  • Speed increases by more (or less) in each successive time interval.

  • Positive curvature → acceleration increasing; negative curvature → acceleration decreasing.

Exam Tips & Tricks

Tip 1: Look at the slope of the graph – that’s your acceleration.

Tip 2: If the graph is a straight line, constant acceleration is guaranteed.

Tip 3: For a curved graph, note whether the slope is getting steeper or flatter to decide if acceleration is increasing or decreasing.

Tip 4: Use the formula \$a = \dfrac{\Delta v}{\Delta t}\$ to calculate the exact value if required.

Tip 5: Remember that a negative slope means the object is slowing down (decelerating).

Quick Analogy: 🚗 Car on a Highway

- Constant acceleration: The driver presses the gas pedal steadily, so the car’s speed rises at a steady rate.

- Changing acceleration: The driver first presses hard, then eases off – the speed increases quickly at first, then more slowly.

- Deceleration: The driver steps on the brakes, so the speed decreases at a steady rate (negative acceleration).

Practice Question

A car’s speed-time graph shows a straight line from 0 s to 10 s, with speed increasing from 0 m/s to 50 m/s.

  1. Is the acceleration constant or changing?

  2. Calculate the acceleration.

Answer: (a) Constant acceleration. (b) \$a = \dfrac{50-0}{10-0} = 5\,\text{m/s}^2\$.