- Difficulty
- Introductory
- Suggested time
- 2 min
- Marks
- 1
The definition of the derivative practice question 2
A particle moves along a line with position metres at time seconds. Find its average velocity over the interval from to .
Give the answer in metres per second.
Which two positions matter here, and how much time passes between them?
Average velocity is displacement over elapsed time: .
A number.
Theory UBC Math 100 §3.2CLP-1 §1.2Key results
Worked solution
Strategy
Average velocity over an interval is the change in position divided by the change in time, which is also the slope of the secant line through the two points on the position graph.
Working
Position at each end of the interval.
Displacement over elapsed time.
Answer
The answer is 9 metres per second.
Check
For a quadratic position the average velocity over an interval is the velocity at its midpoint, and s′(2.5) = 2·2.5 + 4 = 9.
Where this goes wrong
Dividing by 4 instead of by the length of the interval, 3, or averaging the two positions. Average velocity is a difference quotient, not an average of values.
Leans on
Slope of a line through two points, from Functions, graphs and inverses
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