A.1.5—Instantaneous and average values
- Syllabus
- First assessment 2025
- Objective
- —
- Level
- SL
Distinguish Instantaneous and Average Motion
Average values use an interval
Average speed is total distance divided by total time. Average velocity is displacement divided by elapsed time. Average acceleration is change in velocity divided by elapsed time.
Instantaneous values use one moment
Instantaneous velocity is the tangent gradient on a position–time graph; instantaneous speed is its magnitude and is what an ideal speedometer reports. Instantaneous acceleration is the tangent gradient on a velocity–time graph. Average values instead use a finite interval.
Connect graph quantities
The gradient of a velocity–time graph is acceleration, and the area under it is displacement. A constant acceleration therefore produces a straight-line velocity–time graph.
Common trap
Do not use the average gradient when a question asks for an instantaneous value. Use the tangent at the specified time.
A.1.5 Exam Analysis
Assessment in practice
1–2 marksHow it is assessed
The evidence tests graph transformation from acceleration–time to velocity–time, requiring the correct gradient/integration relationship and recognition of the initial condition.
Command terms
Identify / Determine
What earns marks
For an average value, use the whole interval and the appropriate total quantity. For an instantaneous value, read the tangent gradient at the stated time. In a velocity–time graph, integrate acceleration to obtain the change in velocity before applying the initial condition.
Watch for
Treating the acceleration value as the velocity value, or using the graph height instead of the gradient/area relationship.
Representative question
Question 1
[Maximum number: 1]
The graph shows the variation of the acceleration a with time t of an object moving in a straight line.
Which graph shows the variation of the velocity v of the object with time t ?
A
B
C
D
A