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

@jim_thompson5910

Answer 2

@ganeshie8

Answer 3

Position function
\[\Large f(t) = 2t^2+3t\]
Velocity function (apply derivative)
\[\Large v(t) = f \ ' (t) = 4t+3\]
A = average velocity
\[\Large A = \frac{1}{b-a}\int_{a}^{b}(v(t)dt)\]
\[\Large A = \frac{1}{4-1}\int_{1}^{4}(4t+3)dt\]
I'll let you finish.