The slope of a position-time graph is the velocity
The graph shows a rover's position. What is the rover's position, in m, at t = 6 s?
A cyclist rides along a straight bike path at a steady 1.5 m/s. At 1 s she is 1 m past the start line. At 5 s she is 7 m past it. Every second of riding adds the same 1.5 m to her position.
Her ride as a position-time graph. The height of the line gives where she is: at 3 s the line sits at 4 m, her position.
Now look at the line's steepness instead of its height. The line climbs 1.5 m during every 1 s of the ride. That is exactly how fast she rides. The steepness of the line, the rise it makes in each second, is called its slope. Her line's slope is +1.5 m/s.
The same line with its climb stepped out: 1.5 m of rise in every 1 s.
That slope is more than a fact about the drawing. It is her velocity, sign included.
The slope of a position-time graph at a moment is the velocity at that moment, sign included.
The slope of a car's position-time graph at t = 5 s is -3 m/s. What is the car's velocity at t = 5 s?
Riding back just as fast, her line drops 1.5 m each second. Slope: −1.5 m/s. Her velocity is −1.5 m/s, because moving back toward the start line counts as negative.
One line now carries two separate readings, and they answer different questions.
One line, two separate facts: the height gives her position; the slope gives her velocity.
Keep the two apart. At one moment a hiker's position-time graph reads x = +50 m, and the slope there is −1 m/s. The height, +50 m, is the hiker's position, not the velocity. The slope gives the velocity: −1 m/s. The hiker sits far out on the positive side while moving in the negative direction.
Keep the two readings apart: the height of the line gives the position; the slope of the line gives the velocity.
At one moment a river boat's position-time graph reads x = +40 m and its slope there is -2 m/s. What is the boat's velocity at that moment?
Your turn
Which feature of a position-time graph gives an object's velocity at a moment?
On a bus's position-time graph, the slope at t = 2 s is +5 m/s and the slope at t = 9 s is -5 m/s. How does the bus's velocity compare between the two moments?
A classmate says a drone must be moving fastest at the moment its position-time graph is highest. Which graph feature actually gives the drone's speed at a moment?