In a particle accelerator, the position vector of a particle...

In a particle accelerator, the position vector of a particle is initially estimated as $\vec{r}=6.0 \hat{\mathrm{i}}-7.0 \hat{\mathrm{j}}+3.0 \hat{\mathrm{k}}$ and after $10 \mathrm{~s}$, it is estimated to be $\vec{r}=-3.0 \hat{\mathrm{i}}+9.0 \hat{\mathrm{j}}-3.0 \hat{\mathrm{k}}$, all in meters. In unit vector notation, what is the average velocity of the particle?

Key Concepts

Unit Vector Notation

Unit vector notation is a method used to express vectors by breaking them down into their component parts along defined coordinate axes. Each component is multiplied by a unit vector (commonly denoted as i, j, and k in three-dimensional space), which simplifies vector arithmetic and communicates directional information clearly.

Time Interval

The time interval is the duration over which a change in position occurs. It is essential for calculating rates of change, such as velocity, as it provides the temporal context for motion.

Average Velocity

Average velocity is a vector quantity defined as the displacement divided by the time interval over which the displacement occurs. It combines both the direction and the speed of the overall change in position and is a fundamental concept in kinematics.

Position Vector

A position vector represents the location of a point in space relative to an origin. It defines the coordinates of a particle's location and is typically expressed in terms of unit vectors along mutually perpendicular axes, providing both a magnitude and direction in a given coordinate system.

Displacement

Displacement is the vector that represents the change in position of an object. It is calculated by subtracting the initial position vector from the final position vector and takes into account both the magnitude and the direction of the change, regardless of the path traveled.

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