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Tutorial: Right Hand Sums

This tutorial is almost identical to the left hand sum tutorial.

We will work with an example. You can download the Excel File for this example.

The following data is in the given file showing velocity (in feet per second) at time t (given in seconds):

 
A
B
C
1
t
v
 
2
0
1.8
 
3
0.7
1.2
 
4
1.4
0.9
 
5
2.1
0.2
 
6
2.8
-0.3
 
7
3.5
-1.0
 
8
4.2
-0.2
 
9
4.9
0.7
 
10
5.6
1.6
 
11
 

In this case, we have entered times t given in seconds in column A and velocities v in feet per second in column B. We know that a left hand sum for velocity will approximate distance traveled.

A Right Hand Sum for a given set of data is calculated:
RHS = SUM (delta t first subinterval * v1 + delta t second subinterval * v2 + delta t third subinterval * v3 + delta t fourth subinterval * v4 + . . . + delta t nth subinterval * vn).

Next, we determine the width of each subinterval. We have readings every 0.7 seconds, and as the velocities are in feet/sec, the units agree.
So delta t is 0.7 seconds. (We would have to adjust this if the velocity were given in other units, such as feet/minute or miles/hour.)

We are approximating the Total Change in Distance Traveled between time = 0 and 5.6 seconds with a Right Hand Sum.
Our RHS = delta t *(v(0.7) + v(1.4) +v(2.1) + . . . + v(5.6))

To do this in Excel:
1. Choose an empty cell below the table,B13, for example.
2. Enter the formula =0.7*SUM(B3:B10).

3. Hit Return. The result printed in B13 is 2.17, so we conclude that the object moved about 2.17 feet in 5.6 seconds..

 

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