# Finding acceleration from a position vs. time

1. Oct 5, 2015

### Detinator10

1. The problem statement, all variables and given/known data
Given the following graph of displacement vs time for an object moving in a straight line (assume const accel):
Find the acceleration between t=0 and t=4

2. Relevant equations
A= ((vi-vf)/2)/time

3. The attempt at a solution
I've tried find the area of t=0 to t=4 in order to convert to velocity and then to acceleration. However, the problem is I don't know how to find the area because the graph is curved. I tried getting the area above the line and subtracting it from the total area of t=0 to t=4. This didn't work because I can't find the area of the hypothetical circle of which the area above the line would be a fraction of. Thanks

P.S. I know there are other questions that ask the same thing but they are either irrelevant to my particular question or went unanswered

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2. Oct 5, 2015

### krackers

Since you are given displacement vs. time, the derivative at a point will give you the velocity. Taking a derivative of the velocity graph gives you the acceleration.

Since the displacement graph is roughly quadratic on [0, 4] the second derivative will be a constant.

Thus you can find the instantaneous velocity at any two points, take their difference, and divide by time to get the acceleration.