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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the formula for finding acceleration is final velocity, minus initial velocity, all over time. So if you have the acceleration and initial speed, which is equal to the initial velocity, you must also have time in order to find the final velocity. Once you have the time, you multiply it by the acceleration. That product gives you the difference of the final velocity and initial velocity, so then you just add the initial velocity to the product to find the final velocity.
Use the formula Acceleration = (final velosity - initial velocity)/ time.
You use the information you're given, along with the equations and formulas you know that relate distance, time, speed, and acceleration, to calculate the number you're asked to find. And here's a tip: Chances are that the initial acceleration, the final acceleration, and the acceleration all along the way, are all the same number.
Yes.
The final velocity is (the initial velocity) plus (the acceleration multiplied by the time).