Question

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Answer 1

Given

$h(t)=10+50t+\frac{1}{2}at^2$

h'(1.25)=9.75 ft/sec

Find

The value of a

Explanation

as we have given h'(1.25)=9.75 ft/sec

so , we need to find the first derivative.

$\begin{gathered} h(t)=10+50t+\frac{1}{2}at^2 \\ \\ h^{\prime}(t)=50+\frac{1}{2}(2at) \\ h^{\prime}(t)=50+at \end{gathered}$

now substitute the values ,

$\begin{gathered} h^{\prime}(1.25)=50+a(1.25) \\ 9.75=50+a(1.25) \\ \\ -\frac{40.25}{1.25}=a \\ \\ -32.2=a \end{gathered}$

Final Answer

Therefore, the value of a is -32.2 ft/sec^2