I am trying to find an instantaneous speed of a car s = 4.4t^2. I have all my steps drawn out in the attached image. It looks like I am off by half but I don't see why yet or how to adjust things.

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- October 26th 2013, 09:33 PMsepotoInstantaneous speed of a car.
I am trying to find an instantaneous speed of a car s = 4.4t^2. I have all my steps drawn out in the attached image. It looks like I am off by half but I don't see why yet or how to adjust things.

Attachment 29589 - October 26th 2013, 09:56 PMchiroRe: Instantaneous speed of a car.
Hey sepoto.

The instantaneous speed is the magnitude of the derivative of the displacement which is s = f(t) = 4.4*t^2 evaluated at that particular time-point.

In a limit form it is f'(x) = lim h-> 0 [f(x+h) - f(x)]/h and represents the slope between a point and some infinitesimally small point just after it (this is why the limit is h->0 since it is close to zero but not exactly zero).

You can also represent the limit as

[f(b) - f(a)]/[b-a] as b->a when b > a

which is what you were getting at (except you didn't use the right limit). - October 26th 2013, 10:11 PMsepotoRe: Instantaneous speed of a car.
Yes I in limit form then the f'(x) formula represents the slope of a secant line? OK also for b and a I did read that in my notes. Are you saying I made a mistake by using 0 in my calculations of t? How can I fix my error?

- October 26th 2013, 11:23 PMibduttRe: Instantaneous speed of a car.
- October 26th 2013, 11:36 PMsepotoRe: Instantaneous speed of a car.
This was so helpful. Thank you very much. I understand much more now.