Calculating Displacement in Relative Motion

In summary: However, if the bus were to start from rest and the passenger were to walk to the front of the bus at the same speed as the bus was moving, then the sum of the displacements would be 2 m, and the speed would be 2 m/s.
  • #1
Balsam
226
8

Homework Statement


A person on a bus walks to the front of the bus at 3.0 km/h relative to the bus, while the bus travels south at 15km/h. What is the passenger's total displacement?

Homework Equations


displacement= final position-initial position
total displacement=displacement1+displacement2

The Attempt at a Solution


Do you draw vectors to do this? I have no clue what to do.
 
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  • #2
Is that the exact problem statement word for word? I ask because it's not possible to calculate the displacement without more information.

Meanwhile try working out how fast the passenger is traveling (with respect to the ground).
 
  • #3
CWatters said:
Is that the exact problem statement word for word? I ask because it's not possible to calculate the displacement without more information.

Meanwhile try working out how fast the passenger is traveling (with respect to the ground).

The question
CWatters said:
Is that the exact problem statement word for word? I ask because it's not possible to calculate the displacement without more information.

Meanwhile try working out how fast the passenger is traveling (with respect to the ground).
The question asks for the passesnger's velocity relative to the road, but I was unsure about how to find displacement because you need displacement to calculate velocity.
 
  • #4
Balsam said:
The question

The question asks for the passesnger's velocity relative to the road, but I was unsure about how to find displacement because you need displacement to calculate velocity.
No, you don't. Velocity is a vector quantity. Vector quantities can be added and subtracted vectorially.
 
  • #5
SteamKing said:
No, you don't. Velocity is a vector quantity. Vector quantities can be added and subtracted vectorially.

So how would you calculate the velocity, because the question only gives you 2 speed values?
 
  • #6
Balsam said:
So how would you calculate the velocity, because the question only gives you 2 speed values?
Read the problem statement carefully again. It doesn't give you just speed; a direction is also specified for the travel of the bus and the person walking in the aisle.

Speed + Direction = Velocity.
 
  • #7
SteamKing said:
Read the problem statement carefully again. It doesn't give you just speed; a direction is also specified for the travel of the bus and the person walking in the aisle.

Speed + Direction = Velocity.
I thought velocity was the rate at which an object is displaced while speed is the rate at which an object changes position-- doesn't that mean that you can't add a direction to speed and turn it into a velocity value, because they're not the same? Ex. An object that takes two seconds to move from a starting position forwards 2m and back 2m has a speed of 2m/s, but it has a velocity of 0m/s because it's not being displaced- I don't know if that's true, but that's what I think.
 
  • #8
Balsam said:
I thought velocity was the rate at which an object is displaced while speed is the rate at which an object changes position-- doesn't that mean that you can't add a direction to speed and turn it into a velocity value, because they're not the same? Ex. An object that takes two seconds to move from a starting position forwards 2m and back 2m has a speed of 2m/s, but it has a velocity of 0m/s because it's not being displaced- I don't know if that's true, but that's what I think.
Displacement is a change in position. It is a vector.
Distance is a change in position. It is a scalar.

http://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement

Nothing is said in the problem about the bus going backwards and forwards. As far as you know, the bus is traveling south at 15 km/hr till the end of time. The guy in the aisle is walking forward at 3 km/hr relative to the bus. If you were standing on the side of the road as this bus and passenger passed you, what would be the speed of the passenger relative to you?
 
  • #9
SteamKing said:
Read the problem statement carefully again. It doesn't give you just speed; a direction is also specified for the travel of the bus and the person walking in the aisle.

Speed + Direction = Velocity.

Balsam said:
I thought velocity was the rate at which an object is displaced while speed is the rate at which an object changes position-- doesn't that mean that you can't add a direction to speed and turn it into a velocity value, because they're not the same? Ex. An object that takes two seconds to move from a starting position forwards 2m and back 2m has a speed of 2m/s, but it has a velocity of 0m/s because it's not being displaced- I don't know if that's true, but that's what I think.

What you are saying is true. (Average) speed = sum of the absolute values of displacement, divided by the total trip time. The summation is over the separate "legs" of the journey. In your example, the speed on the forward portion is 2 m/s, so the displacement is 2t (m) (where t = forward trip time in seconds). The displacement on the backward portion is 2t as well; t must be the same because the distances and speeds are the same on both legs of the trip. So, the total absolute displacement = 2t + 2t = 4t, while the total trip time = 2t; thus, speed = 4t/2t = 2 (m/s). And, of course, velocity = 0, just as you said.
 
  • #10
Thats not relevant to this problem.

Velocity has two components, speed and direction.

The problem statement contains all the info needed to work out both components on their own. No need to add the two components.

Some examples of velocity...

100mph heading North.

60 meters per second vertically upwards.

4kts heading west along the equator.
 
  • #11
CWatters said:
Thats not relevant to this problem.

Velocity has two components, speed and direction.

The problem statement contains all the info needed to work out both components on their own. No need to add the two components.

Some examples of velocity...

100mph heading North.

60 meters per second vertically upwards.

4kts heading west along the equator.
So wouldn't the person's velocity just be 3km/h[N]? If so, what was the point of the bus' speed being given?
 
  • #12
Balsam said:
So wouldn't the person's velocity just be 3km/h[N]? If so, what was the point of the bus' speed being given?
According to you, the problem asks for the passenger's velocity relative to the road. This is why Item No. 1 in the HW template asks posters to provide a complete problem statement.

CWatters said:
Thats not relevant to this problem.

Velocity has two components, speed and direction.

The problem statement contains all the info needed to work out both components on their own. No need to add the two components.
Emphasis added.
Except, according to Post #3, the problem asks for the passenger's velocity relative to the road.
 
  • #13
SteamKing said:
Except, according to Post #3, the problem asks for the passenger's velocity relative to the road.

I agree. I think the OP was confused by..

SteamKing said:
Speed + Direction = Velocity.

eg It's not regular addition.
 

Related to Calculating Displacement in Relative Motion

What is displacement?

Displacement is the change in position of an object from its original location to its final location.

How do you calculate displacement?

Displacement can be calculated by subtracting the initial position from the final position. It is represented by the symbol Δx (delta x).

What is the difference between displacement and distance?

Displacement is a vector quantity that includes both magnitude (size) and direction, while distance is a scalar quantity that only includes magnitude. Displacement takes into account the starting and ending points of an object's motion, while distance only measures the total length traveled.

Can displacement be negative?

Yes, displacement can be positive, negative, or zero. It depends on the direction of the object's motion relative to its starting point. A negative displacement indicates that the object has moved in the opposite direction from its starting position.

What are the units for displacement?

The SI unit for displacement is meters (m). However, it can also be measured in other units such as feet, centimeters, or kilometers depending on the scale of the object's motion.

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