Chapter 2, Problem 53A

To determine

To find:Whether a person can determine the object’s instantaneous velocity and average velocity with the given data.

Answer to Problem 53A

Instantaneous velocity cannot be determined by the given data but the average velocity can be determined.

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:

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

Instantaneous velocityis the velocity of the object at any instant of time or at any point of its path of motion.

Instantaneous velocity can be given as:

  $\begin{array}{l}v=\underset{\Delta t\to 0}{Lt}\frac{\Delta x}{\Delta t}\\ v=\frac{dx}{dt}\end{array}$

To calculate the instantaneous velocity at any point one should know the variation of velocity with respect to time or position. It cannot be determined with the knowledge of net displacement or total time taken by an object.

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 can be given as:

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

Conclusion:

With the help of given data, a person is able to find the average velocity but cannot find the instantaneous velocity.