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Equations of Motion
When you are given a graph, look at the axies and see the things being measured!! i.e. velocity over time
The gradients of graphs are useful at determining average/values at a point in time.
It gives the derivative of the y axis, i.e. for displacement time graph it gives velocity
The area under a curve gives the opposite of the gradient, i.e. tells us the overall change.
It gives the anti-derivative of the y axis, i.e. for velocity/time graph you get change in displacement from the area under the curve.
Notice change in, not simply the displacement. The graph could indicate a point in time where the object has already been displaced, so from the beginning of the graph the only information we can gather from the area under the curve is the change in displacement, and not the overall displacement.
Equations
$v_{av} = \frac{s}{t}$ - this is an average, velocity may not be constant!
