Average acceleration given velocity points?

syeh
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How do you find average acceleration given a table with points of velocity (ft/sec)?

t (sec): 0 15 30 45 60
v(t) (ft/sec):0 40 60 70 75

the question asks: Find the average acceleration of Rocket A over t=[0,60] seconds.


I used change in v(t)/change in time to find 4 points of acceleration (2.667, 1.333, .667, .333). I added those and divided by 4 to get 1.25. But I do not think that is how to solve the problem.
 
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syeh said:
How do you find average acceleration given a table with points of velocity (ft/sec)?

t (sec): 0 15 30 45 60
v(t) (ft/sec):0 40 60 70 75

the question asks: Find the average acceleration of Rocket A over t=[0,60] seconds.


I used change in v(t)/change in time to find 4 points of acceleration (2.667, 1.333, .667, .333). I added those and divided by 4 to get 1.25. But I do not think that is how to solve the problem.

You just find the quotient (v(60)-v(0))/(60-0). That's average acceleration.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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