An automobile is driven down a straight highway such that after 0 ≤t ≤12 seconds it is s=4.5 t^2

Name: Problem 28, Chapter 2: Calculus Early Transcendentals
Uploaded: 2020-12-02T01:27:10-08:00
Duration: 1 min 30 s
Channel: Carson Merrill
Description: An automobile is driven down a straight highway such that after 0 ≤t ≤12 seconds it is s=4.5 t^2 feet from its initial position. (a) Find the average velocity of the car over the interval [0,12] . (b) Find the instantaneous velocity of the car at t=6

step 1 So first we want to start off by graphing this model that we have. It's s equals 4 .5 t squared.

Question

An automobile is driven down a straight highway such that after $0 \leq t \leq 12$ seconds it is $s=4.5 t^{2}$ feet from its initial position. (a) Find the average velocity of the car over the interval $[0,12] .$ (b) Find the instantaneous velocity of the car at $t=6$

   An automobile is driven down a straight highway such that
after $0 \leq t \leq 12$ seconds it is $s=4.5 t^{2}$ feet from its initial
position.
(a) Find the average velocity of the car over the interval
$[0,12] .$
(b) Find the instantaneous velocity of the car at $t=6$

Calculus Early Transcendentals

Howard Anton, Irl… 9th Edition

Chapter 2, Problem 28

Instant Answer

Solved by Expert Carson Merrill

12/02/2020

Step 1

The total distance travelled is given by the function $s=4.5t^{2}$ evaluated at $t=12$, which is $s=4.5(12)^{2}=648$ feet. The total time taken is $12$ seconds. Therefore, the average velocity is $\frac{648}{12}=54$ ft/s. Show more…

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An automobile is driven down a straight highway such that after $0 \leq t \leq 12$ seconds it is $s=4.5 t^{2}$ feet from its initial position. (a) Find the average velocity of the car over the interval $[0,12] .$ (b) Find the instantaneous velocity of the car at $t=6$

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Key Concepts

Displacement Function

A displacement function describes the location of an object as a function of time along a defined path. It provides the basis for analyzing motion by determining how position changes over time, and it can be used to derive other motion-related quantities.

Average Velocity

Average velocity is defined as the total displacement divided by the total elapsed time over a given interval. It provides a measure of the overall rate of change of position, ignoring the details of how the motion may vary within the interval.

Instantaneous Velocity

Instantaneous velocity is the rate of change of the displacement function at a specific moment in time. It is determined by taking the derivative of the displacement function, which gives the exact velocity at any given point.

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