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]. Include units in your answer.

Question

danjs · Answer

a line from end point to endpoint, the slope of tha tsecant

tkhunny · Answer

Well, do it. How far has it travelled, starting at hour #1 and ending at hour #4?

anonymous · Answer

would i plug in one into this equation or the derivative?

danjs · Answer

makes it a smooth change in position over change in time value with constant slope/velocity. over the whole time interval

danjs · Answer

you have the position function,   a slope value on that graph is the change in position/change in time,   aka  velocity

danjs · Answer

the derivative is for instantaneous values, not average

anonymous · Answer

can you find 4 instantaneous values and then average them

danjs · Answer

you want a secant slope,  not the tangent slope to the curve

tkhunny · Answer

You can find infinitely many instantaneous values and average them.  Oh, wait, that's just the same as evaluating the function.

danjs · Answer

[f(4) - f(1) ]  /  ( 4 - 1)

anonymous · Answer

now what?

tkhunny · Answer

Knowing when you're done is important.

danjs · Answer

the position function is a parabola

f(t) = 2t^2+3t

average velocity from t=1 to t=4 , will be the slope of a line connecting those two endpoints on the curve

slope - [f(b)-f(a)] / (b - a)    
for the interval [a,b]

danjs · Answer

miles / hr

anonymous · Answer

so the slope is [f(4) - f(1) ]  /  ( 4 - 1)

anonymous · Answer

@DanJS

danjs · Answer

yeah , two points

(1 , f(1))  and  (4 , f(4))