Calculating Distance Using Trapezoid Rule: A Scientific Approach

[kfulton]

Homework Statement

A city bus accelerates as it leaves one stop, then decelerates as it comes to another stop. The chart below measures the velocity v given in miles per hours, between each stop. Find the distance, in miles, the bus travels between every interval (stop) using the trapezoid rule.

Relevant Equations

b-a/n

Here is the problem in it form with chart. The answers are written in and we needed to verify they were correct. We were told they were correct, but I am not getting that answer. I start with 5-0/2 (5)(18). I thought that was first stop and I was way wrong. Not sure how else to do to get the correct answers.

 

[berkeman]

Homework Statement:: A city bus accelerates as it leaves one stop, then decelerates as it comes to another stop. The chart below measures the velocity v given in miles per hours, between each stop. Find the distance, in miles, the bus travels between every interval (stop) using the trapezoid rule.
Relevant Equations:: b-a/n

View attachment 299451 Here is the problem in it form with chart. The answers are written in and we needed to verify they were correct. We were told they were correct, but I am not getting that answer. I start with 5-0/2 (5)(18). I thought that was first stop and I was way wrong. Not sure how else to do to get the correct answers.

I'm not understanding the table. Could you upload a sketch of what you think the velocity profile looks like? And what do the zeros in the first and last boxes mean? I could see if they were the velocity at the very start and end of the trip, but the other boxes are supposed to contain the "velocity between each stop", not the instantaneous velocity at that mile marker...?

 

[Mark44]

I'm not understanding the table.

The velocities represent the bus's velocity between two stops. The zeros at the beginning and end are its velocity at the stops.

Relevant Equations:: b-a/n

I start with 5-0/2 (5)(18). I thought that was first stop and I was way wrong. Not sure how else to do to get the correct answers.

No, the first stop is the last entry in the table. As @berkeman recommended, sketch a graph of v vs. t, and connect the velocity values with straight lines. Those will give you trapezoids that you can use to get an estimate of the total distance between the two stops.

Also, use more parentheses. Your relevant equation, b - a/n is not an equation, and means $b - \frac a n$, which you surely didn't mean. Written as inline text, it should be (b - a)/n.
Further, 5-0/2 (5)(18) would normally be interpreted as $5 - \frac 0 2 * 5 * 18$, which I don't think you intended, either.

For the first written-in entry in the table, the area of the triangle is $\frac 1 2 18 * \frac 1 {12} = \frac 9 {12} = .75$ The 1/12 fraction is 5 minutes, converted to a fractional part of an hour. Most of the other parts of the table can be calculated using trapezoids.

 

[pbuk]

If the numbers are the right answer then almost every word in the question is either misleading or just plain wrong; for instance the words "between each stop" should be "at each time". Where on Earth has this problem come from?