Answer:
The slope of a position-time graph can be calculated as:
where
is the increment in the y-variable
is the increment in the x-variable
We can verify that the slope of this graph is actually equal to the velocity. In fact:
corresponds to the change in position, so it is the displacement,
corresponds to the change in time
, so the time interval
Therefore the slope of the graph is equal to
which corresponds to the definition of velocity.
Answer:
Cosmic ray's frame of reference: 99,875 years
Stationary frame of reference: 501,891 years
Explanation:
First of all, we convert the distance from parsec into metres:
The speed of the cosmic ray is
where
is the speed of light. Substituting,
And so, the time taken to complete the journey in the cosmic's ray frame of reference (called proper time) is:
Converting into years,
Instead, the time elapsed in the stationary frame of reference is given by Lorentz transformation:
And substituting v = 0.98c, we find: