Solving for ds/dt: Is the Answer C?

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SUMMARY

The discussion centers on solving the differential equation ds/dt = dv, with a focus on determining the correct answer to a homework problem. The participant suggests that the answer is C based on observation, but is challenged to provide a more rigorous justification. Key concepts include the use of basic kinematic equations and the relationship between acceleration, velocity, and position. The discussion emphasizes the importance of understanding the shape of velocity and position curves when analyzing motion.

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  • Understanding of basic kinematic equations
  • Familiarity with the concepts of acceleration, velocity, and position
  • Ability to interpret graphs of motion
  • Knowledge of differential equations in physics
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  • Study the basic kinematic equations relating acceleration, velocity, and position
  • Learn how to analyze velocity graphs to determine motion characteristics
  • Explore the implications of constant acceleration on motion curves
  • Practice solving differential equations in the context of physics problems
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Homework Statement



http://puu.sh/c0mFR/515cf5fd15.png

Homework Equations



ds/dt=dv

The Attempt at a Solution


I think answer is C by observation.
Is it correct? if not what is the answer[/B]
 
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You make an unsupported (by formula or calculation) guess and then ask for the answer? I don't think so.

You might consider some of the basic kinematic equations relating acceleration to velocity to position. The velocity graph consists of straight line segments, what does that tell you about the form of equation that would fit them?

Play around with the basics to get a feel for it. For example, assume a constant acceleration so that v = a*t. What's the shape of the velocity curve? The position curve? Can you apply what you find out here?
 

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