question a hummingbird travels along a horizontal line according to the function s(t)=-10t³ - t - 6 where t…

question a hummingbird travels along a horizontal line according to the function s(t)=-10t³ - t - 6 where t is measured in seconds and s is measured in feet. what is the velocity function v(t)? provide your answer below:

question a hummingbird travels along a horizontal line according to the function s(t)=-10t³ - t - 6 where t is measured in seconds and s is measured in feet. what is the velocity function v(t)? provide your answer below:

Answer

Explanation:

Step1: Recall velocity - displacement relation

Velocity is the derivative of displacement. So $v(t)=s^\prime(t)$.

Step2: Differentiate the given function

Given $s(t)=- 10t^{3}-t - 6$. Using the power - rule $\frac{d}{dt}(t^{n})=nt^{n - 1}$, we have: $v(t)=\frac{d}{dt}(-10t^{3}-t - 6)=-10\times3t^{2}-1-0$.

Step3: Simplify the derivative

$v(t)=-30t^{2}-1$.

Answer:

$v(t)=-30t^{2}-1$