How far did the bike travel with acceleration and constant speed?

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Homework Help Overview

The problem involves a bike that accelerates from 0.0 m/s to 5.0 m/s over a period of 4.5 seconds, followed by traveling at a constant speed for another 4.5 seconds. The objective is to determine the total distance traveled by the bike during these two phases.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods to calculate the distance, including using average speed and area under a speed-time graph. Some suggest performing arithmetic with the provided equations and values, while others emphasize the importance of showing workings before arriving at a conclusion.

Discussion Status

Several participants have provided guidance on how to approach the calculations, noting the two distinct phases of motion. There is a recognition of the different methods that can be employed, but no explicit consensus on a single approach has been reached.

Contextual Notes

Participants mention the expectation to show workings as part of the forum's guidelines, and there is a focus on ensuring that all calculations are based on the given equations and values.

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[SOLVED] Acceleration and Distance

Homework Statement


"A bike first accelerates from 0.0m/s to 5.0m/s in 4.5secs, then continues at this constant speed for another
4.5s. What is the total distance traveled by the bike?"


Homework Equations


d = .5 a t^2 + Vi* t
a = V/t
 
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For the first part it would be best to used the average speed to work out the distance.

[tex]s =\left(\frac{u+v}{2}\right) t[/tex]
 
Hey Razored. :smile:

Ok, I am sure there is more than one way to approach this question. I would draw out a speed time graph, with time along the x-axis and time up the y-axis, then calculate the area under the graph. Do you understand that? If not just let me know and I will try and explain. These forums usually ask that you make or show some workings first. :smile:
 
Okay, you have the equations, and you have the numbers. Now do the arithmetic! What is the acceleration if the bike accelerated from 0 to 5 m/s in 4.5 s? Just put the numbers into the second equation. Use the first equation to find the distance the bike traveled in that time.

The second part is easy. When the bike got to 5 m/s it stopped accelerating- it continued at 5 m/s for 4.5 s. How far did it go in the second 4.5 seconds?

Now find the total distance it travelled.
 
I got 34m total, is that correct?
 
razored said:
I got 34m total, is that correct?
Correct with round off.

As others mentioned there are two parts. One period of 4.5 s at constant acceleration and one period of 4.5 s at constant velocity.

During the first period, the average v is 2.5 m/s, so d = 2.5 m/s * 4.5 s, and in the second V = 5 m/s, so d = 5 m/s * 4.5 s.
 
Yep.
 
Thanks.
 
  • #10
Its amazing how much service one can drum up in the chat room.
 
  • #11
^ Haha I know! The question is also nice to do, or atleast I enjoyed it nice a simple. =]
 

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