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zeesbrat3
 one year ago
A particle moves on a line away from its initial position so that after t hours it is s = 2t2 +3t miles from its initial position. Find the average velocity of the particle over the interval [1, 4].
zeesbrat3
 one year ago
A particle moves on a line away from its initial position so that after t hours it is s = 2t2 +3t miles from its initial position. Find the average velocity of the particle over the interval [1, 4].

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zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2@Hero @nincompoop @abb0t @Whitemonsterbunny17 @freckles @ganeshie8 @Miracrown @vera_ewing @jim_thompson5910

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2average rate of change (average velocity) between two points is same as the "slope" of the secant line connecting those two points

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2So find the derivative and set it equal to 0?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2You're given \[s(t) = 2t^2 +3t\] For average velocity in the interval \([1,4]\), you simply find the slope between points \((1,s(1))\) and \((4,s(4))\) : \[\dfrac{s(4)s(1)}{41}\]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2mean value theorem..

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Easy, thats just the slope formula!

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2\[s(4) = 2(4)^2 + 3(4) = 32 + 12 = 44\] \[s(1) = 2 + 3 = 5\] \[\frac{ 44  5 }{ 4 1 } = \frac{ 39 }{ 3 } = 13\]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2Wow! Thank you, as always :)

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 what would be the unit? miles/hour^2?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2how do you measure velocity ?

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{ m }{ s^2 }\]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2I was actually good at physics lol

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2I would normally say that but this problem has hours and miles

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2i lied its just \[\frac{ m }{ s }\]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{ m }{ s^2 }\] is acceleration

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\text{average rate of change}=\dfrac{s(4)s(1)}{41}\] Notice that the units for top is \(miles\) and the units for bottom is \(hours\). so the unit for average rate of change is \(miles/hour\)

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.2So, just switch from metric to american

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2average velocity of the particle over the interval [1, 4] is 13 miles/hour
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