Uniformly Accelerated Rectilinear Motion
Senior 2 · Physics
Uniformly Accelerated Rectilinear Motion
Lesson 4 of 4
25 min
Let's begin
A driving examiner, a coach timing a runner and a GPS tracker on a moto all turn motion into graphs. A graph shows the whole journey at a glance, and two simple rules, slope and area, let you read speed, acceleration and distance straight off it. Graph questions appear in almost every O-level physics paper.
A moto moves along a straight road at a constant 10 m/s.
| t (s) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| s (m) | 0 | 10 | 20 | 30 | 40 |
| v (m/s) | 10 | 10 | 10 | 10 | 10 |
A moto starts from rest and accelerates at 2.0 m/s².
| t (s) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| v (m/s) | 0 | 2 | 4 | 6 | 8 |
| s (m) | 0 | 1 | 4 | 9 | 16 |
A moto starts from rest and speeds up uniformly to 10 m/s in 5 s. It then travels at 10 m/s for 10 s, and finally slows uniformly to rest in 4 s. The v–t graph is a trapezium with corners at (0 s, 0), (5 s, 10 m/s), (15 s, 10 m/s) and (19 s, 0).
Tip
"Slope gives the rate, area gives the total."
Before you answer, read the axis labels. Students often mix up s–t and v–t graphs. A horizontal line on an s–t graph means the object is standing still, but on a v–t graph it means constant velocity.
What does a horizontal line on a displacement–time graph show?
Solution: The displacement is not changing, so the object is at rest (velocity = 0).
A cyclist speeds up from rest to 8 m/s in 4 s, rides at 8 m/s for 6 s, then stops uniformly in 2 s. Find the acceleration in each stage and the total distance.
Solution: The accelerations are 8 ÷ 4 = 2 m/s², then 0, then −8 ÷ 2 = −4 m/s². Distance = ½ × 4 × 8 + 8 × 6 + ½ × 2 × 8 = 16 + 48 + 8 = 72 m.
Describe the v–t graph of a stone dropped from rest, ignoring air resistance.
Solution: It is a straight line through the origin with a gradient of 9.8 m/s² (g). Velocity rises by 9.8 m/s every second.
Why is the s–t graph for uniform acceleration curved, but the v–t graph straight?
Solution: Velocity changes by the same amount each second, so v–t is straight. Displacement grows by a larger amount each second (1 m, then 3 m, then 5 m, and so on), so s–t curves upwards.
Summary
Sources and credits
The Rwandan examples, worked examples and practice items are written by Ganzaa.
