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   $\frac{d (v(t))}{dt} = z [v(t)]^2$

Step-by-step 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

       $a(t) = \frac{d (v(t))}{dt}$

So

     $\frac{d (v(t))}{dt} = z [v(t)]^2$