Steeper means faster
The slope of a position-time graph gives the velocity.
Two lines
Two objects start from the same point. On a position-time graph, one line climbs more steeply than the other.
What do you think the steepness tells us?
What this lesson covers
The idea
The slope (steepness) of a graph gives the rate of change of the Y-axis quantity with respect to the X-axis quantity, so the slope of a position-time graph gives velocity; a steeper line means a higher velocity.
Two lines
Two objects start from the same point. On a position-time graph, one line climbs more steeply than the other.
What do you think the steepness tells us?
- How fast the position is changing
- How heavy the object is
- How long the road is
Measure the slope
Press Next step to compare lines A and B over the same 4 s.
Rise over run
In the same 4 s, A's position changed by 20 m and B's by 40 m. Dividing the change in position by the change in time gave 5 m s⁻¹ for A and 10 m s⁻¹ for B. That ratio is the slope of the line.
The slope (steepness) of a graph gives the rate of change of the Y-axis quantity with respect to the X-axis quantity. So the slope of a position-time graph gives the velocity: a steeper line means a higher velocity.
Notes
The slope of a position-time graph is the velocity. A steeper line means a higher velocity.
Check yourself
The slope of a position-time graph gives…
On a position-time graph, line B is steeper than line A. Which object has the higher velocity?
A straight position-time graph passes through 10 m at 2 s and 50 m at 6 s. What is the velocity (the slope)?
Answer: 10 m s⁻¹
(50 m − 10 m) ÷ (6 s − 2 s) = 40 m ÷ 4 s = 10 m s⁻¹.
What does the slope of a graph give?
- the acceleration. The slope of a velocity-time graph gives the acceleration, not the slope of a position-time graph.
- the position at time zero. The slope is a rate of change, not the starting position.
- the velocity — correct. Yes!
- Object B — correct. Yes!
- Object A. A less steep line means a smaller change in position in the same time, so A has the lower velocity.
- Both have the same velocity. Lines of different steepness have different slopes, so the velocities differ.
- The total length of the line. The slope measures the steepness of the line, not how long it is.
- The rate of change of the Y-axis quantity with respect to the X-axis quantity — correct. Yes!
- The value of the X-axis quantity. The slope compares the change in Y with the change in X. It is not the value of X.