Graphs of Motion · 7.2.4
Solving speed-time graph problems
Students combine everything learnt about speed-time graphs, sketching, finding gradient for acceleration, and finding area for distance, to solve multi-step problems. This often means using a known total distance or total time to work out a missing value, such as an unknown speed, time or acceleration in part of the journey.
The official learning standard (7.2.4)
“Solve problems involving speed-time graphs.”
What it means
Students combine everything learnt about speed-time graphs, sketching, finding gradient for acceleration, and finding area for distance, to solve multi-step problems. This often means using a known total distance or total time to work out a missing value, such as an unknown speed, time or acceleration in part of the journey.
How it is examined
This standard is examined in SPM Paper 2 as a full structured question worth several marks, combining graph-reading, area and gradient calculations. Students may need to find a missing time or speed given the total distance, or compare two stages of motion within the same journey.
Worked example
A van accelerates uniformly from rest to 24 m/s in 6 seconds, travels at this constant speed for t seconds, then decelerates uniformly to rest in 4 seconds. If the total distance travelled is 372 m, find the value of t.
- Distance in acceleration stage = ½ × 6 × 24 = 72 m.
- Distance in deceleration stage = ½ × 4 × 24 = 48 m.
- Distance in constant-speed stage = 24 × t = 24t m.
- Total distance: 72 + 24t + 48 = 372.
- 24t = 372 - 120 = 252, so t = 252 ÷ 24 = 10.5.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I know which formula to use for each part of the graph?
Identify the shape first: a sloped line forms a triangle (Area = ½ × base × height), a horizontal line forms a rectangle (Area = length × width), and a graph with two different horizontal speeds forms a trapezium (Area = ½ × sum of parallel sides × height).
What if the question asks for average speed instead of distance?
Average speed = total distance ÷ total time. First find the total distance using the area under the graph, then divide by the total time taken for the whole journey to get the average speed.
Can the object have two different accelerations in one problem?
Yes, many SPM questions include an acceleration stage and a separate deceleration stage with different gradients. Calculate each gradient (or area) separately using the relevant part of the graph, since each straight-line section represents a single constant acceleration.