# Riemann sums with velocity and distance.

1. Nov 29, 2009

### Wm_Davies

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

I really need help starting this problem as I am not sure what to do.

Your task is to estimate how far an object traveled during the time interval 0t8 , but you only have the following data about the velocity of the object.

time (sec) 0 1 2 3 4 5 6 7 8
velocity (feet/sec) 4 1 -2 -3 -4 -3 -1 -3 -1

To get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something like the black curve in the graph below.

"See the graph pictured below."

You decide to use a left endpoint Riemann sum to estimate the total displacement. So, you pick up a blue pen and draw rectangles whose height is determined by the velocity measurement at the left endpoint of each one-second interval. By using the left endpoint Riemann sum as an approximation, you are assuming that the actual velocity is approximately constant on each one-second interval (or, equivalently, that the actual acceleration is approximately zero on each one-second interval), and that the velocity and acceleration have discontinuous jumps every second. This assumption is probably incorrect because it is likely that the velocity and acceleration change continuously over time. However, you decide to use this approximation anyway since it seems like a reasonable approximation to the actual velocity given the limited amount of data.

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

Total displacement = "I am not even sure what this is refering to"

Total distance traveled =

There is a part B & C ,but I think if I can get some help figuring this out then I can figure out the rest by myself (I hope).

2. Relevant equations

Distance = Time X Velocity

3. The attempt at a solution

I have no attempts because I am not sure how to start this problem.

#### Attached Files:

• ###### Calc graph.png
File size:
2.1 KB
Views:
116
2. Nov 29, 2009

### Wm_Davies

Oh, I forgot to mention that this is for calculus 1.