Question

Write a differential equation that fits the physical description. The at time t is proportional to the power of its .

Answer 1

Complete Question

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Answer:

The differential equation that fits the physical description is
`(d (v(t)))/(dt) = z [v(t)]^2`

Explanation:

From the question we are told that

The acceleration due to air resistance of a particle moving along a straight line at time t is proportional to the second power of its velocity v, this can be mathematically represented as

`a(t) \ \ \alpha \ \ \ [v(t)]^2`

Where
`a(t)` is the acceleration at time t

and
`v(t)` is the velocity at time t

So

=>
`a(t)= z [v(t)]^2`

Where z is a constant

Generally acceleration is mathematically represented as

`a(t) = (d (v(t)))/(dt)`

So

`(d (v(t)))/(dt) = z [v(t)]^2`