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pashok25 [27]
2 years ago
13

What is the formula for finding the time it takes for an object to reach terminal velocity?

Physics
1 answer:
Ivan2 years ago
5 0

Answer:

t=\tau(\tanh^{-1}(\frac{v}{v_t}))

Explanation:

Terminal velocity is the maximum velocity attained by a body when the net upward force on it is equal to the net downward force as it falls through a fluid from a certain height.

The time required to reach terminal velocity is infinite as the object never reaches absolute terminal velocity and always approaches terminal velocity.

The velocity v of a falling object expressed in terms of terminal velocity v_t and time 't' is given as:

v=v_t\tanh(\frac{t}{\tau})

Where, \tau is a constant and has units of time.

Now, expressing the above in terms of time 't', we get:

t=\tau(\tanh^{-1}(\frac{v}{v_t}))

Therefore, the formula to find time to approach terminal velocity is:

t=\tau(\tanh^{-1}(\frac{v}{v_t}))

When the velocity is 76% of terminal velocity, the time taken is \tau.

When the velocity is 96% of terminal velocity, the time taken is 2\tau.

When the velocity is 99.5% of terminal velocity, the time taken is 3\tau and so on..

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