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By the end of this section, you will be able to:
  • Explain the concept of reference frames.
  • Write the position and velocity vector equations for relative motion.
  • Draw the position and velocity vectors for relative motion.
  • Analyze one-dimensional and two-dimensional relative motion problems using the position and velocity vector equations.

Motion does not happen in isolation. If you’re riding in a train moving at 10 m/s east, this velocity is measured relative to the ground on which you’re traveling. However, if another train passes you at 15 m/s east, your velocity relative to this other train is different from your velocity relative to the ground. Your velocity relative to the other train is 5 m/s west. To explore this idea further, we first need to establish some terminology.

Reference frames

To discuss relative motion in one or more dimensions, we first introduce the concept of reference frame     s . When we say an object has a certain velocity, we must state it has a velocity with respect to a given reference frame. In most examples we have examined so far, this reference frame has been Earth. If you say a person is sitting in a train moving at 10 m/s east, then you imply the person on the train is moving relative to the surface of Earth at this velocity, and Earth is the reference frame. We can expand our view of the motion of the person on the train and say Earth is spinning in its orbit around the Sun, in which case the motion becomes more complicated. In this case, the solar system is the reference frame. In summary, all discussion of relative motion must define the reference frames involved. We now develop a method to refer to reference frames in relative motion.

Relative motion in one dimension

We introduce relative motion in one dimension first, because the velocity vectors simplify to having only two possible directions. Take the example of the person sitting in a train moving east. If we choose east as the positive direction and Earth as the reference frame, then we can write the velocity of the train with respect to the Earth as v TE = 10 m / s i ^ east, where the subscripts TE refer to train and Earth. Let’s now say the person gets up out of /her seat and walks toward the back of the train at 2 m/s. This tells us she has a velocity relative to the reference frame of the train. Since the person is walking west, in the negative direction, we write her velocity with respect to the train as v PT = −2 m / s i ^ . We can add the two velocity vectors to find the velocity of the person with respect to Earth. This relative velocity    is written as

v PE = v PT + v TE .

Note the ordering of the subscripts for the various reference frames in [link] . The subscripts for the coupling reference frame, which is the train, appear consecutively in the right-hand side of the equation. [link] shows the correct order of subscripts when forming the vector equation.

The vector equation vector v sub P E equals vector v sub P T plus vector v sub T E is shown. The subscripts P (in v sub P T) and E (in v sub T E) in the sum are linked. The subscripts T (in v sub P T) and T (in v sub T E) in the sum are linked.
When constructing the vector equation, the subscripts for the coupling reference frame appear consecutively on the inside. The subscripts on the left-hand side of the equation are the same as the two outside subscripts on the right-hand side of the equation.

Questions & Answers

what is mass
ilance Reply
it is the quantity of matter in a substance....expressed in Kg as the SI unit.
what is the universe of conductivity
Agbeyangi Reply
what is si unit of force?
Jose Reply
Kg m / s^2 You can see that this is the case from dimensional analysis of F = M a
Newton which is Kgm/s2
What's power in physics
Power is the rate of doing work. P=W/T
A car moving with a velocity of 54km/hr accelerates uniformly at the rate of 2mper seconds. Calculate the distance traveled from the place where acceleration began to where the velocity reaches 72km/hr and the time taken to cover d distance
Betty Reply
t=2.5s and s=43.75m
how to find amplitude of interfering wave
Roha Reply
how do we slove a pendulum clock shaft question
Seray Reply
An object of mass m moves with acceleration a down a rough incline.
Phyu Reply
If the average velocity of an object is zero in some time interval, what can you say about the displacement of the object fr that interval?
what is force
Biggie Reply
you ever seen star wars?
What is angular velocity
Amara Reply
refer to how fast an object rotates ot revolve to another point
An object undergoes constant acceleration after starting from rest and then travels 5m in the first seconds .determine how far it will go in the next seconds
Sophy Reply
what is the deference between precision and accuracy
In measurement of a set, accuracy refers to closeness of the measurements to a specific value, while precision refers to the closeness of the measurements to each other. 
Thank you Mr..
Are there is a difference between Error and Relative Error...
An aircraft flies 300km due east and 600km due north. determine the magnitude of its displacement
Sophy Reply
which formula did you use
what is Fermat principle.
Madhu Reply
find the angle of projection at which the horizontal range is twice the maximum height of a projectile
Akaji Reply
impulse by height fomula
Tigst Reply
what is impulse?
Tigst Reply
impulse is the integral of a force (F),over the interval for which it act
Practice Key Terms 2

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