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: 9780136847243Non è quello che usi tu?Cambia libro di testo

Tutti i libri di testo

Briggs 3rd Edition

Ch. 3 - Derivatives

Problema 3

Capitolo 3, Problema 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 $[2, 3]$ .

Guida verificata passo dopo passo

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} $.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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.

Video consigliato:

Percorso guidato

5:20

Relations and Functions

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.

Video consigliato:

Percorso guidato

06:37

Average Value of a Function

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.

Video consigliato:

Percorso guidato

04:22

Sigma Notation

Pratica correlata

Domanda del libro di testo

Find the slope of the line tangent to the graph of y = tan^−1 x at x= −2.

181

views

Domanda del libro di testo

75–86. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x).

f(x) = (1+ 1/x)^x

145

views

Domanda del libro di testo

75–86. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x).

f(x) = (x+1)¹⁰ / (2x-4)⁸

226

views

Domanda del libro di testo

75–86. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x).

f(x) = (x+1)^3/2(x-4)^5/2 / (5x+3)^2/3

134

views

Domanda del libro di testo

A ship leaves port traveling southwest at a rate of 12 mi/hr. At noon, the ship reaches its closest approach to a radar station, which is on the shore 1.5 mi from the port. If the ship maintains its speed and course, what is the rate of change of the tracking angle θ between the radar station and the ship at 1:30 P.M. (see figure)? (Hint: Use the Law of Sines.) <IMAGE>

289

views

Domanda del libro di testo

Calculator limits Use a calculator to approximate the following limits.

lim x🠂0 e^3x-1 / x

252

views