Relative Motion and Frames of Reference

Relative Motion in One Dimension

​Created by James Pickert

Your Point of View Matters!

When we study motion, it's implied that we describe it from a specific point of view, which we describe as our frame of reference.

Open Ended

Over the next couple of minutes, brainstorm a list of all the things around you that are moving. Don't feel limited to what's in the classroom! We'll discuss your reasoning after the time expires.

Don't forget to submit your answer before time runs out!

Everything is Moving!

There is motion all around us, from the air particles in our atmosphere, to the earth itself as it rotates on its axis and revolves around the sun.

Because everything on the Earth's surface moves at the same rate, we consider anything that is fixed on the Earth's survace to be non-moving.

When we observe motion happening​, we analyze them with respect to a frame of reference that we decide.

This turns the process of analyzing motion into a simple vector addition problem.

Stationary Frame of Reverence

Math Response

You are in a hurry to reach your flight and decide to take the moving walkway to get there faster. You are walking at 3.0 m/s relative to the stationary ground. If the walkway moves at 5.0 m/s in the same direction, how fast would you appear to be moving, in m/s to an observer standing still in the airport? (do not include units in your answer)

Type answer here

Correct Answer: 8

Deg^°

Rad

In a stationary frame of reference...

v_relative = v₁ + v₂ + ... +v_n

So we basically just add the velocity vectors together to find the relative, or apparent, speed of our moving object.

As you drive along the highway, you know that the trees and other objects in your surroundings are not moving.

However, as you drive at a constant speed, if feels like you are standing still while the world around you zooms past, in a way.

​

Moving Frame of Reference

Just like in that first video, we could say that our surroundings are moving relative to us!

Surfin' the Highway

Suppose you are driving in a car, we'll call it Car 2. While driving, you are not moving fast enough for the taste of the driver behind you (Car 1), and they begin to pass your car.

Surfin' the Highway

In this case, since both of you are moving in the same direction, Car 1 appears to be moving slower than it actually is. The difference between your speeds is the relative speed of the car.

v_relative = v₁ - v₂

Where v₁ is the velocity of the object you're observing and v₂ is your velocity.

Opposite directions

This works when moving in opposite directions as well! Since a velocity in the opposite direction would be considered negative, we would add the velocity magnitudes together to find your apparent speed.

v_relative = v₁ + v₂ ; When moving in opposite directions

Where v₁ is the velocity of the object you're observing and v₂ is your velocity.

Closing the distance, Widening the Gap

Knowing our relative velocity can help us figure out how long it would take for two approaching objects to meet one another.

​We simply use v_relative as our velocity, and set the displacement equal to the distance between our approaching objects.

Math Response

Runner X and Y are 10.0 m apart If x = 7 m/s and y = 9 m/s , How long (in seconds) will it take for them to reach one another?

Type answer here

Correct Answer: 0.625

Deg^°

Rad

Math Response

If Car 1 moves at 22.0 m/s and car 2 moves at 20.0 m/s, how long will it take for them to be 45 meters apart?

Type answer here

Correct Answer: 22.5

Deg^°

Rad