How quickly does it change?
Rate of change, and average velocity as one example.
Speeding up from rest
A vehicle starts from rest and speeds up. Its position is noted every 2 s. In the first 2 s it moves only a little. Later it moves much more in the same 2 s.
How could we describe how quickly its position is changing?
What this lesson covers
The idea
The rate of change is the ratio of the change in one quantity to the corresponding change in time; average velocity is the average rate of change of position with respect to time.
Speeding up from rest
A vehicle starts from rest and speeds up. Its position is noted every 2 s. In the first 2 s it moves only a little. Later it moves much more in the same 2 s.
How could we describe how quickly its position is changing?
- Divide the change in position by the time taken
- Add the position and the time
- Look at the final position
Change in position over change in time
Open each tab. Read the change in position and the change in time.
Change divided by time
The same vehicle gave 1 m s⁻¹, 5 m s⁻¹ and 0.5 m s⁻¹ in the three tabs. Each number is a change in position divided by the corresponding change in time. It tells us how quickly the position is changing.
The rate of change is the ratio of the change in one quantity to the corresponding change in time. Average velocity is the average rate of change of position with respect to time.
Notes
Rate of change = change in a quantity ÷ corresponding change in time. Average velocity is the average rate of change of position.
Check yourself
What is a rate of change?
A vehicle's position changes from 4 m to 16 m between 4 s and 8 s. What is the average rate of change of its position?
Answer: 3 m s⁻¹
(16 m − 4 m) ÷ (8 s − 4 s) = 12 m ÷ 4 s = 3 m s⁻¹.
Average velocity is…
The position of an object changes by 30 m in 6 s. What is the average rate of change of its position?
Answer: 5 m s⁻¹
30 m ÷ 6 s = 5 m s⁻¹.
- The total amount of a quantity. A total is not a ratio of a change to a time. A rate of change divides a change by the time in which it happens.
- The ratio of the change in one quantity to the corresponding change in time — correct. Yes!
- The change in time divided by the change in the quantity. This is upside down. The change in the quantity is divided by the change in time.
- the total change in position, without dividing by time. That is the displacement. Average velocity divides it by the time interval.
- the average rate of change of time with respect to position. This is the wrong way round. Velocity tells how position changes with time.
- the average rate of change of position with respect to time — correct. Yes!