How to find maximum force on a velocity vs time graph

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SUMMARY

To determine the maximum force from a velocity versus time graph, apply Newton's second law, F = ma, where mass (m) is constant. The maximum force occurs when the acceleration (a) is at its peak, which corresponds to the maximum slope of the velocity graph. This peak acceleration is identified at the point of inflection, specifically at t = 0.35 seconds, where the concavity shifts from concave down to concave up. Estimating the slope of the graph between v = +0.1 m/s and v = -0.1 m/s provides the necessary acceleration to calculate the maximum force.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Ability to interpret velocity versus time graphs
  • Knowledge of calculus concepts such as derivatives and concavity
  • Familiarity with estimating slopes from graphical data
NEXT STEPS
  • Learn how to calculate acceleration from a velocity versus time graph
  • Study the concept of points of inflection in calculus
  • Explore methods for estimating slopes on graphs
  • Review practical applications of F = ma in physics problems
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Physics students, educators, and anyone interested in understanding the relationship between force, mass, and acceleration through graphical analysis.

AnonymousAnonymous
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Homework type question moved from technical forum, hence template not shown.
The velocity versus time graph is the following:

http://imgur.com/kyebx8H

As the title asks, how would you find the maximum force on a velocity vs time graph given nothing but the graph and the mass of the object in question. My reasoning was that since f = ma and m is never changing, that the time at which the maximum force would be applied when dv/dt is greatest. However, since a function is not provided, one would find this point (in this case, the point of inflection) by finding where the concavity of the function shifts from concave down to concave up, indicating a local maximum (maximum acceleration and therefore maximum force) which is at t=0.35s. I'm stuck on how you would find the maximum force from this and would appreciate any help.
 
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AnonymousAnonymous said:
... f = ma ...dv/dt...I'm stuck on how you would find the maximum force from this ...
You have all you need in your post.
 
AnonymousAnonymous said:
The velocity versus time graph is the following:

http://imgur.com/kyebx8H

As the title asks, how would you find the maximum force on a velocity vs time graph given nothing but the graph and the mass of the object in question. My reasoning was that since f = ma and m is never changing, that the time at which the maximum force would be applied when dv/dt is greatest. However, since a function is not provided, one would find this point (in this case, the point of inflection) by finding where the concavity of the function shifts from concave down to concave up, indicating a local maximum (maximum acceleration and therefore maximum force) which is at t=0.35s. I'm stuck on how you would find the maximum force from this and would appreciate any help.

You should be able to estimate the slope at that point from the graph. It even looks like the curve between v= +0.1 to -0.1 m/s is almost a straight line. So you can easily find the slope.

Zz.
 

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