The relative position we can find the correct answers are:
1. x_ah = -10 miles, Car B x_bh = + 10 miles, Car C x_ch = -30 miles
2. x_ {gb} = -40 miles
3. x_ {ea} = +25 miles
4. The position must be measured in two different times
5. The osition and the time
In physics, the magnitudes must be measured with respect to some reference that is arbitrarily assigned the value zero. Specifically in kinematics and dynamics, it is essential to establish a coordinate system and an explicit reference to perform all measurements.
1) In this case they give a coordinate axis (North - South) regarding where to carry out the measurements, as they ask that the House be the reference point, this point is worth zero, the magnitudes to the right are positive and the magnitudes to the left they are negative; also in the diagram the value of each division is indicated is 5 mile. Therefore the positions of the cars are
Car A x_{ah} = -10 miles
Car B x_{bh} = + 10 miles
Car C x_{ch} = -30 miles
The meaning of the subscripts is that the last index corresponds to the body with respect to which the measurements are made, in the table you will find all nomenclature
Carr Position
x_ {ah} Car A with respect to home (h)
x_ {bh} Car B with respect to home (h)
x_ {ch} Car C with respect to home (h)
2) The position of the gas station relative to B is requested
The relative distance of two objects is the distance of one object measured from the reference of the other body
x_ {bh} = ax_ {gh} + x_ {gb}
where x_{bh} is the distance of car B from the house, x_ {gh} is the distance of the gas station from the house and x_{gb} is the distance of the gas station from B
x_ {gb} = - (x_ {gh} - x_ {bh})
x gb = - [30 - (10)]
x_ {gb} = -40 miles
3) The position of the school (e) with respect to car A is requested
x_ {eh} = 15 miles
x_ {ea} = x_ {eh} + x_ {ah}
x_ {ea} = 15 + 10
x_ {ea} = +25 thousands
4) The average velocity of a body is defined as the change of position with respect to time
In this case, to know if something is moving, the position should be measured in two different times and use the relation
v_ {avg} =
Where v is the average velocity, Δx and Δt are the position and time variations in the interval.
5) From the previous expression we can see that the average velocity depends on two factors: position and time
In conclusion using the relative position we can shorten the correct answers are:
1. x_ah = -10 miles, Car B x_bh = + 10 miles, Car C x_ch = -30 miles
2. x_ {gb} = -40 miles
3. x_ {ea} = +25 miles
4. Measure position in two different time
5. The position and time
Learn more about relative position here: