# Integral velocity/time problem

1. Jul 18, 2010

### phillyolly

I have completed a problem and would like you to check it and see if I got it right.

1. The problem statement, all variables and given/known data
The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Estimate the distance traveled during this period

Here is the graph, where a=40 http://www.webassign.net/scalcet/5-1-016alt.gif

3. The attempt at a solution

You will see a print screen of my work. Did I do correctly that I put together a lower and upper estimates and divided the sum by 2 in order to estimate the distance traveled? I believe I made a mistake.

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2. Jul 18, 2010

### Staff: Mentor

Your endpoints are all wrong. You have 0, .5, 1.0, 1.5, 2.0, 2.5, 3.0. In the graph they are 0, 5, 10, 15, 20, 25, 30 seconds. In both estimates you should have $\Delta t$, not $\Delta x$. x should not appear in your work.

Since the velocities are in km/hr, your time units should be in hours, not seconds. 5 seconds = 5 sec X 1 min/60 sec X 1 hr/60 min = 1/720 hr. This is your $\Delta t$. The distance will be in km.

3. Jul 18, 2010

### phillyolly

Thank you a lot for the notes.

4. Jul 18, 2010

### phillyolly

Here is my revised version. Please can you check this one?
I have two solutions: the first one is for midpoints.
The second one is for lower and upper estimates.

Thanks

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• ###### Lower-upper-estim-solution.jpg
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5. Jul 18, 2010

### Staff: Mentor

You still have quite a few mistakes. In the 2nd image, your summation should go from i = 1 to i = 6, not 2/45. In the second and third images, there are numerous errors in the converted times. From the graph, the times are 0, 5, 10, 15, 20, 25, and 30 seconds.
5 sec = 1/720 hr
10 sec = 2/720 hr
15 sec = 3/720 hr
...
30 sec = 6/720 hr
Several of your reduced fractions are wrong. For example, 6/720 $\neq$ 1/10 hr.

6. Jul 18, 2010

### phillyolly

OK, based on your suggestions, I have completed the assignment. I hope that this time I did it correctly. Please take a look.

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7. Jul 19, 2010

### Staff: Mentor

The three estimates look good. The only thing I would add is the distance units.