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Using both methods (split the difference and equidistant) to determine the value of s prime at a give t. We saw a pattern continue to create our equation for velocity/ s prime.

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Although S has a constant (c), the equation for s prime does not.

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What would s’ be if the formula for a moving object were s=2t2? 

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What would s’ be if the formula for a moving object were s=2t2? 

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The table shows a second difference of 4. I used the average rate of change for the 2 second interval 3 to 5 as 16. Then, I also found the average rate of change for the one second intervals 3 to 4 and 4 to 5, which were 14 and 18 respectively. The average of those intervals ((14+18)/2) also equals 16. If I then use the number that is the second difference (4) and multiply it by 4 seconds, I will again get an s' value of 16. Therefore, the formula for s'=4t

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We found the common second difference of 8, by this point we realized s' was just the common second difference times t. We thought that the +7 at the end of the equation didn't change the outcome of our s' equation because the 7 changed the starting point and not the actual velocity. s'=8t

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The second difference is 8.

S' at t= 3 is 24.

We noticed the coefficient 4 multiplied the coefficient, 2 is 8. And...8*3 is 24 which matches our S' calculation for t=3.

We believe that in general, given s=at^2+c, s' = 2at. We believe c affects position but not velocity.

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We got a second difference of 6. Therefore, s'=6t

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Using both the table and the average rate of change...the s' formula for at2+bt+c would be 2at+b. The c value (the constant) effects starting position, but does not effect velocity.

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Unclear yet on a formula for s'. Using the strategy of "splitting the difference" gives the velocity at any point.