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.

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Timmothy

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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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