Question

A particle p is moving along the x-axis the displacement x metres from O can be writen as x=t^5-12t²+9 find the velocity

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Answer 1

`v = t (5t^(3) - 24)`

Explanation:

We are given an expression to solve for the displacement (x), so in order to find velocity (v), we need to differentiate the function.

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Solving :

⇒
`(dx)/(dt) = (d)/(dx) (t^(5) - 12t^(2) + 9)`

⇒
`v = (5)t^(5-1) - (2)12t^(2-1) + 0`

⇒
`v = 5t^(4) - 24t`

⇒
`v = t (5t^(3) - 24)`

Using this equation, we can find the velocity if a value of t is given.