This is a straightforward problem, but requires a number of unit conversions. To find the speed, we will need to determine the change in distance per unit time:

While we are given distance and time, we need to convert it to meters per second. A distance of is converted to meters with the relation .

Time requires several step-wise conversion. First, convert the hours to minutes.

Find the total number of minutes and convert it to seconds.

Finally, find the total number of seconds.

Use the final distance and final time to calculate the speed in meters per second.

First, when thinking about SI you should usually start with the metric system -- this leaves us with meter and kilometer. The correct SI unit for distance is the meter -- displacement is in meters, velocity is in meters per second, etc.

While a kilometer is a metric unit of distance, the correct SI unit for distance is the meter. When making calculations with length, it is necessary to convert kilometers to meters.

Seconds are the SI unit for time. Ohms are the SI unit for electrical resistance. Farads are the SI unit for capacitance. Teslas are the SI unit for magnetic field strength.

Units are used as the interval by which a given parameter can be measured. SI units are the standardized units that are used universally in physics and chemistry to make calculations consistent. Each parameter has its own SI unit.

Mass is a parameter, not a unit. It is a property of a given system, rather than an interval system. The SI unit for measuring mass is the kilogram.

Decibels are the SI unit for sound intensity, Farads are the SI unit for capacitance, meters are the SI unit for length (distance and displacement), and seconds are the SI unit for time.

The difference between a scalar and a vector is that a vector requires a direction. Scalar quantities have only magnitude; vector quantities have both magnitude and direction. Time is completely separated from direction; it is a scalar. It has only magnitude, no direction.

Force, displacement, and acceleration all occur with a designated direction.

Important distinctions to know:

Speed is a scalar, while velocity is a vector.

Distance is a scalar, while displacement is a vector.

Force and acceleration are vectors. Time is a scalar.

A vector has both magnitude and direction, while a scalar has only magnitude. Ask yourself, "for which of these things is there a direction?" For displacement, we would say "50 meters NORTH," whereas with the others, we would say "50 meters," "20 seconds," or "30 miles per hour."

Important distinctions to know:

Speed is a scalar, while velocity is a vector.

Distance is a scalar, while displacement is a vector.

Force and acceleration are vectors. Time is a scalar.

Displacement is a vector quantity; the direction that Michael travels will be either positive or negative along an axis. We are being asked to solve for his position relative to his starting point, NOT for the distance he has walked.

First we need to find his total distance travelled along the y-axis. Let's say that all of his movement north is positive and south is negative.

. He moved a net of 5 meters to the north along the y-axis.

Now let's do the same for the x-axis, using positive for east and negative for west.

. He moved a net of 9 meters to the east.

Now to find the resultant displacement, we use the Pythagorean Theorem. The net movement north will be perpendicular to the net movement east, forming a right triangle. Michael's position relative to his starting point will be the hypotenuse of this triangle.

Now take the square root of both sides.

Since the problem only asks for the magnitude of the displacement, we do not need to provide the direction.

Displacement is a vector quantity; it will have both magnitude and direction.

First we need to find his total distance travelled along the y-axis. Let's say that all of her movement north is positive and south is negative.

. She moved a net of 30 meters to the north. 

Now let's do the same for the x-axis, using positive for east and negative for west.

. She moved a net of 29 meters to the east.

Now, to find the resultant displacement, we use the Pythagorean Theorem. Her net movement north will be perpendicular to her net movement east, forming a right triangle. Her location relative to her starting point will be the hypotenuse of the triangle.

Now take the square root of both sides.

Since we are solving for a vector, we also need to find the direction of this distance. We do this by solving for the angle of displacement.

To find the angle, we use the arctan of our directional displacements in the x- and y-axes. The tangent of the angle will be equal to the x-displacement over the y-displacement.

Combining the magnitude and direction of our distance gives us the displacement: .

Since she is running on a circular track, every time she makes a loop she has a total displacement of . Remember, displacement take into account how far you've travelled, it only uses the total change in distance from where you start and where you stop. Using dimensional analysis, we can determine how many laps she runs in 20 minutes.

After twenty minutes, she has made EXACTLY two loops around the track. That means she is starting and stopping in EXACTLY the same place. Her displacement would be , since there is no change between her starting position and her ending position.

Distance is a scalar quantity and will take into account only the number of floors travelled, regardless of the direction of movement.

Walter takes an incredibly complicated path to wash the windows on the building. When calculating distance, we add up all the movement he does, regardless of direction.

First, he travels down one floor (4th to 3rd).

Then he travels up three floors (3rd to 6th).

Then he travels down one floor (6th to 5th), then down another three floors (5th to 2nd).

Finally, he travels down one more floor (2nd to 1st).

In total, Walter travelled .