Acceleration as a function of time

AI Thread Summary
The position of a particle moving along the x-axis is described by the equation x = 6.8t + 5.5t². To find acceleration as a function of time, one must derive the position function twice: the first derivative yields velocity, and the second derivative provides acceleration. The discussion emphasizes the importance of understanding the relationship between displacement, velocity, and acceleration through basic calculus. A common mistake is to solve for a specific time rather than expressing acceleration as a function of time. The correct approach involves obtaining an equation for acceleration rather than a numerical value.
halbe1
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Homework Statement


A particle moves along the x axis. Its position as a function of time is given by x = 6.8t + 5.5t^{2}, where t is in seconds and x is in meters. What is the acceleration as a function of time?



Homework Equations





The Attempt at a Solution

 
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halbe1 said:

Homework Equations


how does acceleration relate to displacement?

OR how are are acceleration and velocity related?

halbe1 said:

The Attempt at a Solution


Do this too.
 
Here's a hint... you can find how to come up with your answer online... It requires BASIC calculus to solve...

Search for how velocity is related to displacement... then search how acceleration is related to velocity... It will tell you what you need to do to the equation you've got to get the answer...

Then do the math and you're done...Hope this helped.
 
Well the slope of velocity is the acceleration.
I tried taking the derivative to find out the time and got 17.8...apparently that's wrong though.
 
Your question isn't asking you for the time... It is asking for the acceleration as a function of time...

Function tells you that your answer will be an equation... not solution of the variable you have left. Go back to what you have before you solved for t.
 
double derivative
derivative of displacement=velocity
derivative of velocity=acceleration
 

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