Chapter 2, Problem 50A

To determine

To Find: The relation between the average velocity of the moving object and its displacement.

Answer to Problem 50A

  $v_{avg}=\frac{x\text{'}-x}{t\text{'}-t}$

Explanation of Solution

Introduction:

Displacement of an object per unit time is called the velocity of the that object. Its SI unit is ${\text{m/s}}^{\text{2}}.$

It can be obtainedby:

  $\text{velocity = }\frac{\text{displacement}}{\text{time}}$

Average velocity is total displacement of the object over time taken by the object.

Let the object starts moving from point $x$ at time $t$ and reached the point $x\text{'}$ at time $t\text{'}$ . Then the average velocity is:

  $\begin{array}{l}{v}_{avg}=\frac{\text{final position - initial position}}{\text{total}\text{time}\text{taken}}\\ v_{avg}=\frac{x\text{'}-x}{t\text{'}-t}\\ v_{avg}=\frac{\text{total displacement}}{\text{total time taken}}\end{array}$

Conclusion:

  $v_{avg}=\frac{x\text{'}-x}{t\text{'}-t}$ is the equation describing how the average velocity of the moving object relates to its displacement.