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

Ch. 3 - Derivatives

Briggs - Calculus: Early Transcendentals 3rd Edition

Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Briggs 3rd Edition

Ch. 3 - Derivatives

문제 3

3장, 문제 3

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 $[2, 3]$ .

검증된 단계별 안내

Identify the formula for average velocity over a time interval [a, b], which is given by the change in position divided by the change in time: $ v_{avg} = \frac{s(b) - s(a)}{b - a} $.

Substitute the given values into the formula. Here, $ a = 2 $ and $ b = 3 $, so the formula becomes $ v_{avg} = \frac{s(3) - s(2)}{3 - 2} $.

Use the provided position values: $ s(2) = 136 $ and $ s(3) = 156 $.

Substitute these values into the equation: $ v_{avg} = \frac{156 - 136}{3 - 2} $.

Simplify the expression to find the average velocity: $ v_{avg} = \frac{20}{1} $.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Position Function

The position function, denoted as s(t), describes the location of an object along a line at a specific time t. It provides a mathematical representation of the object's movement, allowing us to analyze its behavior over time. Understanding this function is crucial for determining other properties, such as velocity and acceleration.

Average Velocity

Average velocity is defined as the change in position divided by the change in time over a specific interval. Mathematically, it is calculated using the formula (s(b) - s(a)) / (b - a), where [a, b] is the time interval. This concept is essential for understanding how fast an object is moving on average during that time period.

Interval Notation

Interval notation is a mathematical way to represent a range of values, often used to specify the domain of a function or the limits of integration. In this context, the interval [2, 3] indicates that we are considering the time from t = 2 to t = 3, inclusive. Recognizing how to interpret and use interval notation is important for solving problems related to motion and calculus.