# Calc 1 Riemann Sums w/ velocity and distance

1. Nov 29, 2009

### Wm_Davies

1. The problem statement, all variables and given/known data

This is somewhat a repost... except I have figured out some of it and I have cleaned up the question.

Your task is to estimate how far an object traveled during the time interval 0<= t >= 8 , but you only have the following data about the velocity of the object.

$$\frac{time (sec)}{velocity (feet/sec)}\frac{0}{4}\frac{1}{1}\frac{2}{-2}\frac{3}{-3}\frac{4}{-4}\frac{5}{-3}\frac{6}{-1}\frac{7}{-3}\frac{8}{-1}$$

"See the attached graph."

(PART 'A') Using the left endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct units.

Total displacement = "I have 11ft which is the right answer."

Total distance traveled = "I cannot figure this out"

2. Relevant equations

Distance = time * velocity
Displacement = time * velocity

3. The attempt at a solution
So I went ahead and got the Riemann sum of the left endpoint on the graph below.

$$\Delta$$X = 1

So I just added the y values.

The sum added up to -11 which was the answer for the displacement. I do not know why this is not the answer for the total distance but maybe I am missing something elementary.

#### Attached Files:

• ###### Graph.jpg
File size:
20.3 KB
Views:
546
Last edited: Nov 29, 2009
2. Nov 29, 2009

### computerex

To find the distance traveled find the area of the shaded region. Area is always positive BTW :D

3. Nov 29, 2009

### Wm_Davies

I tried to compute the area, but I am not getting it. Also area if area is always positive then why would the area of a curve under the x axis be negative?

4. Nov 29, 2009

### computerex

Distance can never be negative.

5. Nov 29, 2009

### Wm_Davies

O.k. that actually makes tons of sense (I figured I was making some elementary mistake). So, I added up the areas as positive numbers and everything was correct. Thanks for the help.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook