zeesbrat3
  • zeesbrat3
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].
Mathematics
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SOLVED
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chestercat
  • chestercat
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zeesbrat3
  • zeesbrat3
@Hero @nincompoop @abb0t @Whitemonsterbunny17 @freckles @ganeshie8 @Miracrown @vera_ewing @jim_thompson5910
zeesbrat3
  • zeesbrat3
any ideas?
zeesbrat3
  • zeesbrat3
help please..

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More answers

ganeshie8
  • ganeshie8
average rate of change (average velocity) between two points is same as the "slope" of the secant line connecting those two points
zeesbrat3
  • zeesbrat3
So find the derivative and set it equal to 0?
ganeshie8
  • ganeshie8
You'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 \((4,s(4))\) : \[\dfrac{s(4)-s(1)}{4-1}\]
zeesbrat3
  • zeesbrat3
mean value theorem..
ganeshie8
  • ganeshie8
Easy, thats just the slope formula!
zeesbrat3
  • zeesbrat3
\[s(4) = 2(4)^2 + 3(4) = 32 + 12 = 44\] \[s(1) = 2 + 3 = 5\] \[\frac{ 44 - 5 }{ 4 -1 } = \frac{ 39 }{ 3 } = 13\]
ganeshie8
  • ganeshie8
Looks good!
zeesbrat3
  • zeesbrat3
That's it?
ganeshie8
  • ganeshie8
Yep.
zeesbrat3
  • zeesbrat3
Wow! Thank you, as always :)
ganeshie8
  • ganeshie8
np
zeesbrat3
  • zeesbrat3
@ganeshie8 what would be the unit? miles/hour^2?
ganeshie8
  • ganeshie8
how do you measure velocity ?
zeesbrat3
  • zeesbrat3
\[\frac{ m }{ s^2 }\]
ganeshie8
  • ganeshie8
Really ?
zeesbrat3
  • zeesbrat3
I was actually good at physics lol
zeesbrat3
  • zeesbrat3
I would normally say that but this problem has hours and miles
zeesbrat3
  • zeesbrat3
i lied its just \[\frac{ m }{ s }\]
zeesbrat3
  • zeesbrat3
\[\frac{ m }{ s^2 }\] is acceleration
ganeshie8
  • ganeshie8
\[\text{average rate of change}=\dfrac{s(4)-s(1)}{4-1}\] 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
  • zeesbrat3
So, just switch from metric to american
ganeshie8
  • ganeshie8
average velocity of the particle over the interval [1, 4] is 13 miles/hour
zeesbrat3
  • zeesbrat3
Okay, thank you :)

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