Question

Average velocity The function $s(t)$ represents the position of an object at time $t$ moving along a line. Suppose $s(2)=136$ and $s(3)=156 .$ Find the average velocity of the object over the interval of time [2,3].

   Average velocity The function $s(t)$ represents the position of an object at time $t$ moving along a line. Suppose $s(2)=136$ and $s(3)=156 .$ Find the average velocity of the object over the interval of time [2,3].

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 2, Problem 7

Instant Answer

Solved by Expert Rakesh Kumar Sharma

05/31/2020

Step 1

The average velocity is calculated by taking the difference in position divided by the difference in time. Mathematically, it can be represented as: $$v_{avg} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}$$ where $s(t_2)$ and $s(t_1)$ are the positions at times $t_2$ and Show more…

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Average velocity The function $s(t)$ represents the position of an object at time $t$ moving along a line. Suppose $s(2)=136$ and $s(3)=156 .$ Find the average velocity of the object over the interval of time [2,3].

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Key Concepts

Average Velocity

Average velocity measures the overall rate of change of position with respect to time over a specific interval. It is calculated as the difference in the object's positions at the endpoints of the interval divided by the time elapsed, providing a single value that represents the object's overall motion during that time period.

Difference Quotient

The difference quotient is the mathematical expression used to compute the average rate of change of a function between two points. In the context of kinematics, it involves calculating the change in position divided by the change in time, which is essential for determining the average velocity over a given time interval.

Position Function

A position function describes the location of an object along a line (or in space) as a function of time. It is a fundamental concept in kinematics that allows one to track an object's movement by assigning a numerical value (its position) to each moment in time.

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