Acceleration: guy and a student are competing against each other

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SUMMARY

The discussion centers on a race scenario where a guy starts running before a student, covering 100 meters, and they finish simultaneously. The key conclusion is that the student must run at least twice as fast as the guy to achieve this, given that he starts running only after the guy has covered half the distance. The mathematical representation of their speeds is expressed as S'(t) = G'(t), indicating that there exists at least one point in time after the student starts running where their speeds are equal.

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Julia Maria
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Homework Statement


A guy and a student are competing against each other in a 100m long race. The guy start before the student. When the guy is halfway the student start running. They are finishing at the same time. We assume that at any time we can talk about their speed.

Show that you and the guy have exactly the same rate of at least one time point after the boy started to run.
How much information do you need to complete the task?

Homework Equations



S`(t) = G`(t)

The Attempt at a Solution



Since the guy started before the student. The student has to run twice as fast to finish at the same time. So his acceleration has to pass the guy acceleration at one time. ( Imagine a graph.
and when they finish at the start line.
They also have the same speed when they both start, but they do not start at the same time. So it is not valid since its not at the same time.

So how can I show this and when do they have the same speed. Am I on the right track?
 
Last edited:
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Julia Maria said:

Homework Statement


A guy and a student are competing against each other in a 100m long race. The guy start before the student. When the guy is halfway the student start running. They are finishing at the same time. We assume that at any time we can talk about their speed.

Show that you and the guy have exactly the same rate of at least one time point after the boy started to run.
How much information do you need to complete the task?

Homework Equations



S`(t) = G`(t)

The Attempt at a Solution



Since the guy started before the student. The student has to run twice as fast to finish at the same time. So his acceleration has to pass the guy acceleration at one time. ( Imagine a graph.
and when they finish at the start line.
They also have the same speed when they both start, but they do not start at the same time. So it is not valid since its not at the same time.

So how can I show this and when do they have the same speed. Am I on the right track?
Hello Julia Maria. Welcome to PF!

The guy travels 50m in the same time that the student 100m. How do their average velocities compare over this time interval?
 
Average velocity is the rate of change of displacement with time.
Δr=50m
v=Δr/Δt Average velocity for the boy
v=(2*Δr)/Δt For the student

So the students average velocity. is twice the boys.

So how do I show when they have the same rate?
And Î`m missing the time to complete the task?
 

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