Please solve. ### Physics Problem: Average Velocity of a Particle**Problem Statement:**The velocity of a particle moving along the x-axis is given by the equation:\[ v(t) = 2 - t^2 \]for time $ t > 0 $.**Question:**What is the average velocity of the particle from time $ t = 0 $ to time $ t = 3 $?(Page reference: Introduction to Motion in One Dimension)**Detailed Explanation:**To find the average velocity, $ v_{avg} $, of the particle over a time interval from $ t = 0 $ to $ t = 3 $, we use the formula:\[ v_{avg} = \frac{1}{t_f - t_i} \int_{t_i}^{t_f} v(t) \, dt \]where $ t_i $ is the initial time, $ t_f $ is the final time, and $ v(t) $ is the velocity function.In this case:- $ t_i = 0 $- $ t_f = 3 $- $ v(t) = 2 - t^2 $Substitute the given values into the average velocity formula to compute the result.For more insights and detailed concepts, refer to our [Motion in One Dimension](#) section.

The velocity of the particle is given as,

Answered: The velocity of a particle moving along…

The velocity of a particle moving along the x- axis is given by v (t) = 2 — t² for time ₺ > 0. What is the average velocity of the particle from time t = 0 to time t = 3?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter6: Rates Of Change

Section6.1: Velocity

Problem 2SBE: Sign of VelocityWhen directed distance is decreasing, is velocity positive or negative? What is the...

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Please solve.

### Physics Problem: Average Velocity of a Particle

**Problem Statement:**

The velocity of a particle moving along the x-axis is given by the equation:
\[ v(t) = 2 - t^2 \]
for time $ t > 0 $.

**Question:**
What is the average velocity of the particle from time $ t = 0 $ to time $ t = 3 $?

(Page reference: Introduction to Motion in One Dimension)

**Detailed Explanation:**

To find the average velocity, $ v_{avg} $, of the particle over a time interval from $ t = 0 $ to $ t = 3 $, we use the formula:
\[ v_{avg} = \frac{1}{t_f - t_i} \int_{t_i}^{t_f} v(t) \, dt \]
where $ t_i $ is the initial time, $ t_f $ is the final time, and $ v(t) $ is the velocity function.

In this case:
- $ t_i = 0 $
- $ t_f = 3 $
- $ v(t) = 2 - t^2 $

Substitute the given values into the average velocity formula to compute the result.

For more insights and detailed concepts, refer to our [Motion in One Dimension](#) section.

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