A biologist looking through a microscope sees a bacterium at r⃗1=2.2 +3.7 -1.2 k μm . After 6.2

step 1 So in this exercise, we have the position of a bacterium at two different times. So they're give

A biologist looking through a microscope sees a bacterium at...

A biologist looking through a microscope sees a bacterium at $\vec{r}_{1}=2.2 \hat{\imath}+3.7 \hat{\jmath}-1.2 k \mu \mathrm{m} .$ After $6.2 \mathrm{s},$ it's located at $\vec{r}_{2}=4.6 \hat{\imath}+1.9 \hat{k} \mu \mathrm{m} .$ Find (a) its average velocity, expressed in unit vectors, and (b) its average speed.

A biologist looking through a microscope sees a bacterium at $\vec{r}_{1}=2.2 \hat{\imath}+3.7 \hat{\jmath}-1.2 k \mu \mathrm{m} .$ After $6.2 \mathrm{s},$ it's located at
$\vec{r}_{2}=4.6 \hat{\imath}+1.9 \hat{k} \mu \mathrm{m} .$ Find (a) its average velocity, expressed in unit vectors, and (b) its average speed.

Key Concepts

Position Vector

A position vector specifies the location of a point in space relative to an origin. It is generally expressed in terms of its components along the coordinate axes using unit vectors, which simplifies the process of calculating differences between points in space.

Displacement

Displacement is the vector difference between the final position and the initial position of an object. It represents both the magnitude and direction of the change in position, and it is calculated by subtracting the initial position vector from the final position vector.

Time Interval

The time interval is the duration over which the displacement occurs. It is an essential component in calculating rates of change such as average velocity and average speed.

Average Velocity

Average velocity is defined as the displacement vector divided by the corresponding time interval. It provides both the magnitude and the direction of the overall change in position over a period of time.

Average Speed

Average speed is a scalar quantity that represents the total distance traveled divided by the time interval during which the motion occurred. Unlike average velocity, average speed does not include directional information.

Unit Vectors

Unit vectors are vectors of length one used to indicate the direction along the coordinate axes. They are crucial in expressing vector quantities in a consistent manner by providing a standard basis for the components of any vector.

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