Question

Equivalent constant velocity Consider the following velocity functions. In each case, complete the sentence: The same distance could have been traveled over the given time period at a constant velocity of ______. $$v(t)=2 t+6, \text { for } 0 \leq t \leq 8$$

   Equivalent constant velocity Consider the following velocity functions. In each case, complete the sentence: The same distance could have been traveled over the given time period at a constant velocity of ______.
$$v(t)=2 t+6, \text { for } 0 \leq t \leq 8$$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 6, Problem 50

Instant Answer

Solved by Expert Kevin Luu

07/19/2020

Step 1

To do this, we take the integral of the velocity function from 0 to 8. The integral of $v(t) = 2t + 6$ is $\int_{0}^{8} (2t + 6) dt$, which is equal to $t^2 + 6t$ evaluated from 0 to 8. Show more…

Show all steps

Thanks for your feedback!

Equivalent constant velocity Consider the following velocity functions. In each case, complete the sentence: The same distance could have been traveled over the given time period at a constant velocity of ______. $$v(t)=2 t+6, \text { for } 0 \leq t \leq 8$$

Play audio

Feedback

Kevin Luu and 98 other subject Calculus 2 / BC educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Constant Velocity

This concept refers to a situation where an object moves at an unchanging speed in a fixed direction. When considering motion problems, replacing a variable velocity with a constant one simplifies calculations, particularly when determining overall distance traveled, by using the average velocity over a time interval.

Average Velocity

Average velocity represents the total displacement divided by the total time taken. It is often used to find an equivalent constant velocity that would result in the same displacement as a variable velocity function over a specific time period.

Definite Integral in Kinematics

In physics and kinematics, the definite integral of a velocity function over a time interval is used to calculate the total displacement. This process sums up the contributions of velocity over time, which is essential for finding distances when dealing with non-constant rates of change.

Please give Ace some feedback