# Thread: Instantaneous speed of a car.

1. ## Instantaneous 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.

2. ## Re: 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).

3. ## Re: 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?

5. ## Re: Instantaneous speed of a car.

This was so helpful. Thank you very much. I understand much more now.