Physics and Math 1.3 Displacement and Velocity

What is the displacement of a man who walks 2 km east, then 2 km north, then 2 km west, and then 2 km south?

His displacement is 0 because the man ends up where he started. However his total distance traveled is 8 km.

What is the relationship between instantaneous velocity and instantaneous speed? Between average velocity and average speed?

Instantaneous speed is the magnitude of the instantaneous velocity vector. Average speed and average velocity may be unrelated because speed does not depend on displacement, but is rather the total distance traveled divided by time.

True or False: Total distance traveled can never be less than the total displacement.

True. Displacement considers the most direct route between two points. Distance will always be equal or larger in magnitude than displacement.

Provide a definition for displacement or velocity in terms of the other variable.

Velocity is the rate of change of the displacement of an object. Displacement is a function of velocity acting over a period of time.

In one year, the Earth travels roughly 940 million kilometers, but its displacement is 0. What is the average speed and average velocity of the Earth?

avg. speed: v = 9.4 x 10⁸ km/3.16 x 10⁷ s = 29.8 km/s avg. velocity: v = 0 km/3.16 x 10⁷ s = 0 km/s

Distance

is a scalar quantity that reflects the path traveled.

Instantaneous velocity

is the limit of the change in displacement over time as the change in time approaches zero.

Instantaneous speed

is the magnitude of the instantaneous velocity vector.

Average velocity

is the total displacement divided by the total time.

Average speed

is the total distance traveled divided by the total time.

Displacement

is the vector representation of a change in position. It is path independent and is equivalent to the straight line distance between the start and end locations

Velocity

is the vector representation of the change in displacement with respect to time.

Instantaneous velocity equation

v = lim ∆t → 0 (∆x/∆t) where v is the instantaneous velocity, ∆x is the change in position, and ∆t is the change in time.

Average velocity equation

v = ∆x/∆t where v is the average velocity, ∆x is the change in position, and ∆t is the change in time.