Set 1 Problem number 7

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s), Extension

• Figure(s)

Problem

While under observation, an object moves 4.695 meters. If the total time of observation is 20.95848 seconds, then what is the average velocity of the object?

Solution

4.695 meters in 20.95848 seconds is 4.695/ 20.95848 meters in 1 second.

• The answer is therefore ( 4.695 meters) / ( 20.95848 seconds) = 4.464 meters per second.

Generalized Solution

Generalized Response: Average velocity is average displacment per unit of time.

• If displacement is `ds and the time interval is `dt, then `ds / `dt is the average displacement per time unit.
• Thus vAve = `ds / `dt.

We also recognize this as the average rate at which position changes.

In this problem we simply think in terms of ratios. 

• We 'feel' average velocity as the ratio of displacement to elapsed time. 
• Just as we know to divide the money we earn by the number of hours it takes to earn it, when we are familiar with the concept of velocity we don't have to quote equations--we simply know to divide displacement by elapsed time.

Explanation in terms of Figure(s), Extension

We can again use the triangular diagram to depict the relationship among `ds, `dt and vAve.

• In this case we can use vAve = `ds / `dt.

This in fact is usually taken as the definition of average velocity. It coincides with the concept of average velocity as average rate of change of position.

Figure(s)