MHB 34 MVT - Application of the mean value theorem

karush
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$10 min = \dfrac{h}{6}$
So
$a(t)=v'(t)
=\dfrac{\dfrac{(50-30)mi}{h}}{\dfrac{h}{6}}
=\dfrac{20 mi}{h}\cdot\dfrac{6}{h}=\dfrac{120 mi}{h^2}$
Hopefully 🕶
 
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karush said:


$10 min = \dfrac{h}{6}$
So
$a(t)=v'(t)
=\dfrac{\dfrac{(50-30)mi}{h}}{\dfrac{h}{6}}
=\dfrac{20 mi}{h}\cdot\dfrac{6}{h}=\dfrac{120 mi}{h^2}$
Hopefully 🕶

The average acceleration is $\displaystyle \frac{20}{\frac{1}{6}} = 120 \,\textrm{mi}/\textrm{h}^2 $

Since the function is continuous and smooth, there must be some value $c \in \left[ 0, \frac{1}{6} \right] $ such that $a\left( c \right) = 120 $ by the Mean Value Theorem.
 
Karush, what you said was simply that the average acceleration was120. In order to correctly answer the question, you have to appeal to the "Mean Value Theorem" as Prove It did.
 
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