- #1

- 129

- 0

## Homework Statement

Given the function

*s(t)*= -16t

^{2}+ 100t which represents the velocity of an object in meters, what is the instantaneous velocity at t = 3 seconds?

## Homework Equations

I think these are correct:

Average velocity equals the slope of the secant line connecting any two points on the graph if there is acceleration is not 0 (i.e., the graph is curved or exponential). (If acceleration is 0, so that the graph of the position vs. time graph is linear, just take the slope of the line.)

Instantaneous velocity equals the slope of the line tangent to a point on the graph

Instantaneous velocity also equals:

lim

*f(a)*

x→a

## The Attempt at a Solution

I did the slope for secant lines connecting the following pairs of time points:

2, 3

2.9, 3

2.99, 3

2.999, 3

2.9999, 3

The respective slopes went from:

20

5.6

4.16

4.016

4.0016

So I am postulating the limit at 3 is 4. So instantaneous velocity at 3 seconds is 4 m/s.

However, if I do:

lim (-16t

^{2}+ 100t)

x→3

I get 156. So the instantaneous velocity at 3 seconds is 156 m/s.

What am I doing wrong? Is the instantaneous velocity at 3 seconds 4 m/s or 156 m/s?