A proper speed-time graph is one in which time is plotted on the horizontal axis and the speed of the object under study is plotted on the vertical axis.
In fact, what you will come across is most likely to be a radial-speed time graph. In such a graph, the speed depicted is the speed away from of towards the origin (or point of reference) or the component of speed in the radial direction. Movement across that direction is likely to be ignored.
Also, to be of real use, you need a velocity time graph, which takes account of the direction of travel.
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Acceleration is indicated on a speed/time graph.
No. The slope on a speed vs time graph tells the acceleration.
It represents the speed of a moving object at any time covered by the graph.
Slope of the graph will give you speed.
The slope of the speed-vs-time graph is the magnitude of acceleration.