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Motion of a Particle - Max Acceleration

Attachment 29044

Given:

What is the max acceleration on the interval: ? - Answer = 21

Logic: When the graph has a maximum value, then it's derivative will be . So of at maximum points. You simply find which of these points lies within the given interval.

So, - Note is random made up term.

- Solve for t. See which values like within

and would be our acceleration value after plugging into

Now test for max or min using 2nd derivative test:

That is positive so our answer of is a minimum and the graph is concave up.

In this case how to find the maximum?

Re: Motion of a Particle - Max Acceleration

Since you found the minimum, and given that a(t) is a parabola, you know that the function increases as you move away from t=1. So simply check the boundary points of t=0 and t=3.

Re: Motion of a Particle - Max Acceleration

Quote:

Originally Posted by

**ebaines** Since you found the minimum, and given that a(t) is a parabola, you know that the function increases as you move away from t=1. So simply check the boundary points of t=0 and t=3.

Thanks, makes sense.