What does the slope of a position-time graph at a moment give?
A delivery van rolls onto a freeway on-ramp. At t = 1 s it is moving at 3 m/s. The driver holds the pedal steady, and by t = 5 s the van is moving at 11 m/s. The van is accelerating the whole way, and you've already seen the equation for that: a = Δv/Δt. The van's trip shows both of the equation's ingredients in one picture.
The rise of the line between two moments is Δv, the change in velocity. The run beneath that rise is Δt, the time the change takes. Rise divided by run is the line's slope, and Δv divided by Δt is the acceleration. The slope and the acceleration are the same division.
On a velocity-time graph, what does the slope of the line at a moment give?
A rising line has a positive slope, so the acceleration is positive. That holds on either side of the axis: a line rising from −7 m/s toward −1 m/s has a positive slope too, so that acceleration is also positive.
A falling line has a negative slope, so the acceleration is negative.
A flat line has zero slope. The velocity is not changing, so the acceleration is zero, however large the velocity itself is. A freight train's line sitting flat at 12 m/s shows a = 0.
The graph shows a car's velocity. What is the sign of the car's acceleration during the interval shown?
The graph shows a shuttle bus's velocity, flat at 5 m/s from t = 2 s to 8 s. What is the bus's acceleration during that stretch?
The graph shows a taxi's velocity over 8 s. During which interval is the size of the taxi's acceleration greatest?
A student sees a graph with one straight rising line and says the object shown must be accelerating. On which kind of graph is the student right?
The graph shows a cargo drone's velocity as a straight line falling from -2 m/s to -8 m/s. What is the sign of the drone's acceleration?