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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].

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  1. zeesbrat3
    • one year ago
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    @Hero @nincompoop @abb0t @Whitemonsterbunny17 @freckles @ganeshie8 @Miracrown @vera_ewing @jim_thompson5910

  2. zeesbrat3
    • one year ago
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    any ideas?

  3. zeesbrat3
    • one year ago
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    help please..

  4. ganeshie8
    • one year ago
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    average rate of change (average velocity) between two points is same as the "slope" of the secant line connecting those two points

  5. zeesbrat3
    • one year ago
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    So find the derivative and set it equal to 0?

  6. ganeshie8
    • one year ago
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    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 \((4,s(4))\) : \[\dfrac{s(4)-s(1)}{4-1}\]

  7. zeesbrat3
    • one year ago
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    mean value theorem..

  8. ganeshie8
    • one year ago
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    Easy, thats just the slope formula!

  9. zeesbrat3
    • one year ago
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    \[s(4) = 2(4)^2 + 3(4) = 32 + 12 = 44\] \[s(1) = 2 + 3 = 5\] \[\frac{ 44 - 5 }{ 4 -1 } = \frac{ 39 }{ 3 } = 13\]

  10. ganeshie8
    • one year ago
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    Looks good!

  11. zeesbrat3
    • one year ago
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    That's it?

  12. ganeshie8
    • one year ago
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    Yep.

  13. zeesbrat3
    • one year ago
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    Wow! Thank you, as always :)

  14. ganeshie8
    • one year ago
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    np

  15. zeesbrat3
    • one year ago
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    @ganeshie8 what would be the unit? miles/hour^2?

  16. ganeshie8
    • one year ago
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    how do you measure velocity ?

  17. zeesbrat3
    • one year ago
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    \[\frac{ m }{ s^2 }\]

  18. ganeshie8
    • one year ago
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    Really ?

  19. zeesbrat3
    • one year ago
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    I was actually good at physics lol

  20. zeesbrat3
    • one year ago
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    I would normally say that but this problem has hours and miles

  21. zeesbrat3
    • one year ago
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    i lied its just \[\frac{ m }{ s }\]

  22. zeesbrat3
    • one year ago
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    \[\frac{ m }{ s^2 }\] is acceleration

  23. ganeshie8
    • one year ago
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    \[\text{average rate of change}=\dfrac{s(4)-s(1)}{4-1}\] Notice that the units for top is \(miles\) and the units for bottom is \(hours\). so the unit for average rate of change is \(miles/hour\)

  24. zeesbrat3
    • one year ago
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    So, just switch from metric to american

  25. ganeshie8
    • one year ago
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    average velocity of the particle over the interval [1, 4] is 13 miles/hour

  26. zeesbrat3
    • one year ago
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    Okay, thank you :)

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