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You cannot find the initial velocity from an acceleration-time graph on its own. What you can do is find the change in velocity over the first T units of time. This is the area under the a-t graph from t = 0 to t = T. This may be a simple calculation of the area of a rectangle or a trapezium or may require integration. But, like all integrations, you end up with an unknown constant - in this case the initial velocity. You must have some additional information - usually a boundary condition - that allows you to find this constant and so the initial velocity.

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Q: How do you find the initial velocity from an acceleration -time graph?
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