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profgabs05

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- Homework Statement
- A mass 𝑚 is accelerated by a time-varying force 𝛼 𝑒𝑥𝑝(−𝛽𝑡)𝑣3, where v is its velocity. It also experiences a resistive force 𝜂𝑣, where 𝜂 is a constant, owing to its motion through the air. The equation of motion of the mass is therefore

𝑚𝑑𝑣/𝑑𝑡= 𝛼 𝑒𝑥𝑝(−𝛽𝑡)𝑣^3 − 𝜂𝑣.

Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity 𝑣0

- Relevant Equations
- 𝑚𝑑𝑣/𝑑𝑡= 𝛼 𝑒𝑥𝑝(−𝛽𝑡)𝑣^3 − 𝜂𝑣.