Question

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].

Answer 1

@Hero @nincompoop @abb0t @Whitemonsterbunny17 @freckles @ganeshie8 @Miracrown @vera_ewing @jim_thompson5910

Answer 2

any ideas?

Answer 3

help please..

Answer 4

average rate of change (average velocity) between two points is same as the "slope" of the secant line connecting those two points

Answer 5

So find the derivative and set it equal to 0?

Answer 6

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 \((4,s(4))\) :

\[\dfrac{s(4)-s(1)}{4-1}\]

Answer 7

mean value theorem..

Answer 8

Easy, thats just the slope formula!

Answer 9

\[s(4) = 2(4)^2 + 3(4) = 32 + 12 = 44\]
\[s(1) = 2 + 3 = 5\]
\[\frac{ 44 - 5 }{ 4 -1 } = \frac{ 39 }{ 3 } = 13\]

Answer 10

Looks good!

Answer 11

That's it?

Answer 12

Yep.

Answer 13

Wow! Thank you, as always :)

Answer 14

np

Answer 15

@ganeshie8 what would be the unit? miles/hour^2?

Answer 16

how do you measure velocity ?

Answer 17

\[\frac{ m }{ s^2 }\]

Answer 18

Really ?

Answer 19

I was actually good at physics lol

Answer 20

I would normally say that but this problem has hours and miles

Answer 21

i lied its just \[\frac{ m }{ s }\]

Answer 22

\[\frac{ m }{ s^2 }\] is acceleration

Answer 23

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

Answer 24

So, just switch from metric to american

Answer 25

average velocity of the particle over the interval [1, 4] is 13 miles/hour

Answer 26

Okay, thank you :)