How to calculate instantaneous acceleration?

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SUMMARY

The discussion focuses on calculating instantaneous acceleration using a velocity-time graph. It establishes that since the acceleration is uniform, the instantaneous acceleration equals the average acceleration. The specific calculation provided indicates that the instantaneous acceleration at 35 seconds is -1.667 m/s², derived from the slope of the graph between 30 seconds and 40 seconds. The tangent line equation is emphasized as a key concept in determining instantaneous acceleration.

PREREQUISITES
  • Understanding of velocity-time graphs
  • Knowledge of the concept of slope in physics
  • Familiarity with the definition of instantaneous acceleration
  • Basic skills in unit conversion (e.g., m/s² to km/h)
NEXT STEPS
  • Study the principles of calculus related to instantaneous rates of change
  • Learn how to derive tangent lines on graphs
  • Explore uniform acceleration and its implications in physics
  • Review examples of velocity-time graphs and their corresponding acceleration calculations
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Students studying physics, educators teaching kinematics, and anyone interested in understanding motion and acceleration concepts.

treyh
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This is the graph and question:
http://img193.imageshack.us/img193/3489/physicquestion.jpg

I cannot seem to find the instantaneous acceleration. I must be doing it wrong because I'm pretty sure to find the the inst. acceleration all i need to know is the tangent line equation.

I've tried a bunch of answers but can't seem to get it right. I need to express the answer in m/s^2 and not km/h but that is easy to convert.

I haven't had much physics experience. How do i find the instantaneous acceleration?

Thanks
 
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Since the acceleration is uniform, instantaneous acceleration = average acceleration.

acceleration = slope of v-t graph

from the graph, the slope of the graph during time = 30s to 40s is a straight line (that means the slope is not varying), that means the acceleration uniform.

so the instantaneous acceleration at time = 35s :
= [(60/3.6) - 0 / (30 - 40)] = -1.667 m/s^2.
 
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treyh said:
I'm pretty sure to find the the inst. acceleration at t = 35 seconds [/color] all i need to know is the tangent line equation.
That's correct, so what is the definition of instantaneous acceleration and what is the slope of that line at t = 35 s?
 

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