Calculating the constant acceleration

AI Thread Summary
An automobile accelerates from 40 m/s to 80 m/s over a distance of 200 m, prompting a discussion on calculating constant acceleration. Two approaches were attempted: one involving time calculation, which led to an incorrect acceleration of 8.0 m/s², and another that directly applied the velocity-position relationship, yielding the correct acceleration of 12 m/s². The validity of assuming the initial position as xi=0 was confirmed as acceptable for this calculation. The consensus is that time is not necessary for solving this problem, as the constant acceleration equation suffices. The discussion emphasizes the importance of using the appropriate equations for motion without needing to determine time.
thushanthan
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Homework Statement



An automobile moving along a straight track changes its velocity from 40 m/s to 80 m/s in a distance of 200 m. What is the (constant) acceleration component of the vehicle during this time?

Homework Equations





The Attempt at a Solution



I try to solve this problems with 2 different approaches.

First :

Since we don't know the time (t) , we need to calculate the time. If we assume the initial position as xi=0 and VxAvg as 40 m/s , then I am getting t=5 sec. But that doesn't help me to reach the final answer. I ended up with 8.0m/s2.

Second:

If I didn't care about the time(t) and if I use Velocity as a function of position eq ( assuming xi =0 ) then I am getting the correct answer which is 12m/s2.

My question is "Can I assume the initial position is xi=0? IS IT CORRECT?"

Thank you!
 
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Your second method is correct. We don't need the time for this problem, as we can use the constant acceleration equation that relates initial velocity, acceleration, initial location, and final location to final velocity.
 
Thank you o:)
 

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