Galilean transformation problem (Speed)

[Ace.]

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?

 

[Andrew Mason]

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

 

[Ace.]

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?

 

[Doc Al]

Why wouldn't it be +126 m if she is moving forward?

To the cyclist, the ground is moving backwards.

 

[HalfLostAndSearching]

The negative sign in this calculation indicates that the direction of the bicycle's motion is opposite to the direction of the bus. This is known as a relative velocity and is commonly used in Galilean transformations to describe the motion of objects in different reference frames. In this case, the negative sign does not affect the magnitude of the bicycle's speed, which is 2.1 m/s, but it does indicate the direction of its motion. It is important to pay attention to the signs in these types of calculations, as they can provide valuable information about the motion of objects in different reference frames.