Question

The position of a car as a function of time
is given by the values in table

t (seconds) 0 1 2 3 4 5
s (feet) 0 12 16 26 38 56

Find the average velocity for the time period
beginning when t = 3 and lasting 2 seconds.

Answer 1

Can someone walk me through this problem?

Answer 2

Let's throw out the first three values for t and s because they are irrelevant to the problem. We are left with:

t = {3,4,5}
s = {26,38,56}

Understanding that distance = rate * time, we can solve for rate, which is the average velocity. The car travelled (56 - 26) feet between t = 3 and t = 5 so distance = 30. This took two seconds, so time = 2. Therefore:

30 feet = r * 2 seconds
r = 15 feet/second.

Answer 3

the average velocity is the slope formed by using the data as points on a graph: (3,16) and (5,56)

Answer 4

to find this "slope" subtract one point from the other:

s t
(5,56)
-(3,16)
--------
2,40 ; and form a fraction by stacking s/t in this case

slope = 40/2 = 20

Answer 5

Yes but at t = 2, s = 26, not 16. :)

Answer 6

t=2 is outside of the scope of the question

Answer 7

whoops, my bad. I meant t = 3.

Answer 8

ah... i see, the mismatched line messed it up for me :)