A particle moves according to the equation x=10 t^2 , where...

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 2.00 $\mathrm{s}$ to 3.00 $\mathrm{s}$ . (b) Find the average velocity for the time interval from 2.00 to 2.10 $\mathrm{s}$ .

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Key Concepts

Position Function

This is a mathematical expression that defines the location of an object as a function of time. It serves as the basis for analyzing the motion of the object and allows one to derive other properties such as displacement, velocity, and acceleration.

Displacement

Displacement represents the change in the position of an object over a given time interval. It is calculated as the difference between the final and initial positions and is a key component in determining average velocity.

Average Velocity

Average velocity is defined as the total displacement divided by the total time interval. It provides a measure of the overall rate of change of position over a specified period, regardless of the details of the intermediate motion.

Time Interval

A time interval specifies the period over which a measurement, such as average velocity, is calculated. It is essential to correctly determine the start and end times of the interval in order to accurately compute the displacement and the corresponding average velocity.

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