Galilean transformation problem (Speed)

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Homework Statement



A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #1). At a time of 60 s later the friend catches a bus (event #2)
If the distance separating the events is 126 m in the frame of the girl on the bicycle, what is the bicycle's speed?

Homework Equations


u = u' + v




The Attempt at a Solution


u = u' + v
can be written as:
Δx/t = Δx'/t + v
v = Δx/t - Δx'/t
v = 0m/60s - 126m /60s
v = -126 m/ 60s
v = -2.1 m/s

Just wondering if the negative holds any significance? I know we're talking about speed which is scalar but how come the calculation gives a negative?
 

Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
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Homework Statement



A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #1). At a time of 60 s later the friend catches a bus (event #2)
If the distance separating the events is 126 m in the frame of the girl on the bicycle, what is the bicycle's speed?

Homework Equations


u = u' + v




The Attempt at a Solution


u = u' + v
can be written as:
Δx/t = Δx'/t + v
v = Δx/t - Δx'/t
v = 0m/60s - 126m /60s
v = -126 m/ 60s
v = -2.1 m/s

Just wondering if the negative holds any significance? I know we're talking about speed which is scalar but how come the calculation gives a negative?
It should be +2.1 m/s. This is because the Δx' represents the displacement of the second event minus the displacement of the first. So v = 0/60 - (-126/60).

You are using the cyclist's reference frame with the origin at the cyclist to determine u' and the bus stop person's (bsp) reference frame with the bsp at the origin to determine u. There are two events: 1. the origins coincide and 2. the bsp enters the bus.

In the cyclist's frame these events occur at 0 and -126 m. using the direction of v as the +x direction. So Δx' = -126m. In the bsp's frame, they both occur at the origin.

AM
 
  • #3
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In the cyclist's frame these events occur at 0 and -126 m.

Why wouldn't it be +126 m if she is moving forward?
 
  • #4
Doc Al
Mentor
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1,498
Why wouldn't it be +126 m if she is moving forward?
To the cyclist, the ground is moving backwards.
 

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