A particle moves on a line away from its initial position so that after t hours it is s = 6t^2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.

Question

mrnood · Answer

the time interval you are interested in is between 1 hour and 4 hours (how many hours is that?)

find the distance travelled after 4 hours (put 4 in place of t in the equation)
find the distance travelled after 1 hour  (put 1 in place of t in the equation)

so ho far did it travel between 1 and 4 hours

the average velocity is the distance travelled /time elapsed

danjs · Answer

The average Velocity is the slope of a secant line connecting the two points given, (4,s(4)) and (1, s(1))

s(1) = 8  and s(4) = 104

$$ave.~velocity = \frac{ s(4)-s(1) }{ 4-1 } = \frac{ 104-8 }{ 4-1} =\frac{ 96 }{ 3 }=\frac{ 32~miles }{ 1~hour }$$

danjs · Answer

The equation for the line is, 
y - 8 = 32(x-1)

The graph is...

danjs · Answer

attachment

mrnood · Answer

@DanJS

It is not permitted by the CoC to give complete answers.

Whilst your explanation is good and complete it leaves NOTHING for th eOP to contribute, and they will just copy "32 miles/hour" and move on.

ALL the method you used is in my first post - BUT the OP would need to understand and DO the math to get to the answer himself.

He LEARNS from doing - he just ticks a box using your answer.