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

To find the average velocity over the interval [1, 4], we need to determine the change in displacement and time.

The displacement of the particle at time t is given by the equation s = 4t^2 + t. To find the change in displacement over the interval [1, 4], we subtract the displacement at t = 1 from the displacement at t = 4:

s(4) - s(1) = (4(4)^2 + 4) - (4(1)^2 + 1)
= (64 + 4) - (4 + 1)
= 68 - 5
= 63 miles

The change in time over the interval [1, 4] is 4 - 1 = 3 hours.

Therefore, the average velocity is calculated by dividing the change in displacement by the change in time:

Average velocity = (Change in displacement) / (Change in time)
= 63 miles / 3 hours
= 21 miles/hour

Therefore, the average velocity of the particle over the interval [1, 4] is 21 miles/hour.

calc question? LOL

s(4) = 4*16 + 4 = 68 miles
s(1) = 5 miles

distance traveled = 63 miles
time = 4 - 1 = 3 hours

av speed = 63/3 = 21 miles/hour