A 7.8 kg object starting from rest falls through a viscous medium and experiences a resistive force R = −b v, where v is the velocity of the object. The acceleration of gravity is 9.8 m/s 2 . If the object’s speed reaches one-half its terminal speed in 6.56 s, determine the terminal speed.

The terminal voltage is

Explanation:

From the question we are given that the Resistive force R is mathematically represented as

       Where b is a constant  known as drag coefficient

          v is the velocity of the object

The objective of this solution is to obtain the terminal speed and this is mathematically represented as

 Where  m is the mass

               g acceleration due to gravity

As the time changes the velocity of the object change and this can be mathematically represented as

We are told that the  

              So substituting this into the above equation we have

Substituting  m = 7.8 kg

Now substituting this value to get the terminal velocity we have

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