There is an important difference between Distance/Time graphs and Speed/Time graphs. They are illustrated below to help you remember how they work.
Distance/Time Graphs
Gradient of Graph = Distance = Speed
Time
Speed/Time Graphs
Gradient of Graph = Increase in Speed = Acceleration
Time
Area under graph = 1/2 x final speed x time
Area under graph = average speed x time
Area under graph = Distance travelled
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