Question

A particle moves according to the equation $x=10 t^{2}$, where $x$ is in meters and $t$ is in seconds. (a) Find the average velocity for the time interval from $2.0 \mathrm{~s}$ to $3.0 \mathrm{~s}$. (b) Find the average velocity for the time interval from $2.0 \mathrm{~s}$ to $2.1 \mathrm{~s}$.

Name: Problem 4, Chapter 2: Fundamentals of Physics
Uploaded: 2021-06-16T09:05:30-08:00
Duration: 1 min 32 s
Channel: Prabhu Ramji
Description: A particle moves according to the equation x=10 t^2, where x is in meters and t is in seconds. (a) Find the average velocity for the time interval from 2.0 s to 3.0 s. (b) Find the average velocity for the time interval from 2.0 s to 2.1 s.

    A particle moves according to the equation $x=10 t^{2}$, where $x$ is in meters and $t$ is in seconds. (a) Find the average velocity for the time interval from $2.0 \mathrm{~s}$ to $3.0 \mathrm{~s}$.
(b) Find the average velocity for the time interval from $2.0 \mathrm{~s}$ to $2.1 \mathrm{~s}$.

Fundamentals of Physics

David Halliday,… 8th Edition

Chapter 2, Problem 4

Instant Answer

Solved by Expert Prabhu Ramji

06/16/2021

Step 1

Step 1: The average velocity is given by the formula: \[v_{avg} = \frac{x_{f} - x_{i}}{t_{f} - t_{i}}\] where $x_{f}$ and $x_{i}$ are the final and initial positions respectively, and $t_{f}$ and $t_{i}$ are the final and initial times respectively. Show more…

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A particle moves according to the equation $x=10 t^{2}$, where $x$ is in meters and $t$ is in seconds. (a) Find the average velocity for the time interval from $2.0 \mathrm{~s}$ to $3.0 \mathrm{~s}$. (b) Find the average velocity for the time interval from $2.0 \mathrm{~s}$ to $2.1 \mathrm{~s}$.

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Key Concepts

Position Function

A position function expresses the location of a particle along a path as a function of time. It is central to kinematics, allowing one to calculate the particle’s position at any given time by substituting the corresponding time value into the function.

Displacement

Displacement refers to the change in position of a particle, calculated as the final position minus the initial position. This concept is key to determining the average velocity, as it represents the net change in position over the time interval considered.

Average Velocity

Average velocity is defined as the total displacement divided by the time interval over which the displacement occurs. It provides a measure of how fast the position of a particle has changed on average during a specified period, regardless of what happens in between.

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