Determine, qualitatively, from given data or the shape of a distance-time graph or speed-time graph when an object is: (a) at rest (b) moving with constant speed (c) accelerating (d) decelerating

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – Motion (Topic 1.2)

1.2 Motion – Qualitative Interpretation of Graphs

In this section we learn how to decide, from the shape of a distance‑time graph or a speed‑time graph, whether an object is:

  • at rest

  • moving with constant speed

  • accelerating

  • decelerating

Key definitions

• Distance‑time graph: plots distance \$s\$ (vertical axis) against time \$t\$ (horizontal axis).

• Speed‑time graph: plots speed \$v\$ (vertical axis) against time \$t\$ (horizontal axis).

• Acceleration \$a\$ is the rate of change of speed: \$a = \frac{\Delta v}{\Delta t}\$

Interpreting a distance‑time graph

Look at the slope of the curve (rise over run). The slope tells us the speed.

Graph featureInterpretation
Horizontal line (slope = 0)Object is at rest (speed = 0)
Straight line with constant non‑zero slopeObject moves with constant speed. The steeper the line, the greater the speed.
Curved line that becomes steeper with timeObject is accelerating (speed increasing).
Curved line that becomes less steep with timeObject is decelerating (speed decreasing but still moving forward).

Suggested diagram: Sketch of four distance‑time graphs illustrating the four cases above.

Interpreting a speed‑time graph

Here the vertical position directly gives the speed, while the slope gives the acceleration.

Graph featureInterpretation
Horizontal line on the time axis (speed = 0)Object is at rest.
Horizontal line above the time axis (constant speed)Object moves with constant speed. Acceleration = 0.
Straight line with positive slopeObject is accelerating. Slope = acceleration \$a\$ (positive).
Straight line with negative slopeObject is decelerating. Slope = acceleration \$a\$ (negative).
Curved line (slope changing)Acceleration is not constant; the object is still accelerating or decelerating depending on whether the slope is positive or negative at that instant.

Suggested diagram: Four speed‑time graphs showing rest, constant speed, acceleration, and deceleration.

Quick checklist for students

  1. Identify the axes: distance vs. time or speed vs. time.

  2. Look at the vertical position:

    • Zero speed → at rest.

    • Non‑zero constant speed → constant speed.

  3. Examine the slope:

    • Zero slope on a distance‑time graph → at rest.

    • Constant non‑zero slope on a distance‑time graph → constant speed.

    • Increasing slope (getting steeper) → accelerating.

    • Decreasing slope (flattening) → decelerating.

  4. For speed‑time graphs, the slope itself tells you the acceleration:

    • Positive slope → accelerating.

    • Negative slope → decelerating.

    • Zero slope → constant speed (or rest if the speed value is zero).

Worked example

Problem: A car’s distance‑time graph shows a straight line from \$t = 0\$ s to \$t = 5\$ s, then a curve that becomes steeper from \$t = 5\$ s to \$t = 10\$ s. Describe the motion.

Solution:

  • From \$0\$ s to \$5\$ s the line is straight with constant slope → the car moves with constant speed.

  • From \$5\$ s to \$10\$ s the line curves and the slope increases → the car is accelerating.

Summary table

Graph typeFeature indicating restFeature indicating constant speedFeature indicating accelerationFeature indicating deceleration
Distance‑timeHorizontal line (slope = 0)Straight line, non‑zero constant slopeCurve that becomes steeper (slope increasing)Curve that becomes less steep (slope decreasing but still positive)
Speed‑timeLine on the time axis (speed = 0)Horizontal line above the axis (speed constant)Positive slope (straight or curved)Negative slope (straight or curved)

Using these visual cues, you can quickly decide the state of motion of any object from its graphs, a skill required in the Cambridge IGCSE Physics examination.