Write a differential equation that fits the physical description. The acceleration due to air resistance acceleration due to air resistance of a particle moving of a particle moving along a straight line along a straight line at time t is proportional to the secondsecond power of its velocity v. The differential equation, with proportionality constant k, is __.

Question

Mathematics

Shawn Matthews

8 September, 06:01

Write a differential equation that fits the physical description. The acceleration due to air resistance acceleration due to air resistance of a particle moving of a particle moving along a straight line along a straight line at time t is proportional to the secondsecond power of its velocity v. The differential equation, with proportionality constant k, is __.

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Answers (1)

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Kendrick Garcia · Answer 1

d/dt (dx/dt) = K (dx/dt) ^2

Step-by-step explanation:

Since, a is proportional to v^2; and a=d/dt (dx/dt) and v = dx/dt since they are instantanious acceleration and velocity respectively.

K = (d^x/dt^2) (dt/dx) ^2