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# User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s$t$, this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v$t$. A body has a time function that determines its position in meters at time t as S$t$=t.³√t+2.t . Present the speed of this body at time t = 8 s.

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## Answer to a math question User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s$t$, this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v$t$. A body has a time function that determines its position in meters at time t as S$t$=t.³√t+2.t . Present the speed of this body at time t = 8 s.

Timmothy
4.8
1. Find the Velocity Function v$t$: The velocity function v$t$ is the derivative of the position function s$t$ with respect to time t. s\left$t\right$=t^{\frac{3}{2}}+2t Applying the power rule and the derivative of a constant term, we get: v\left$t\right$=\frac{3}{2}t^{\frac{1}{2}}+2 2. Evaluate v$t$ at t=8 seconds: Now, substitute t=8 into the velocity function v$t$ to find the velocity at t=8 seconds: v\left$8\right$=\frac{3}{2}8^{\frac{1}{2}}+2=8 Therefore, at t=8 seconds, the velocity of the body is 8m/s.
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