A particle moves on a straight line away from its initial position so that after t seconds its position is given by s = 2T(squared) + 3T in feet from its initial position.
a. Find the average velocity of the particle between 2 and 5 seconds.
b. Use the derivative to find the instantaneous velocity of the particle at T=1 second and T=8 seconds.

Question

A particle moves on a straight line away from its initial position so that after t seconds its position is given by s = 2T(squared) + 3T in feet from its initial position.
a. Find the average velocity of the particle between 2 and 5 seconds.
b. Use the derivative to find the instantaneous velocity of the particle at T=1 second and T=8 seconds.

perl · Answer

average velocity on [a,b] is 
[s(b) - s(a)] / ( b - a)

perl · Answer

so you can plug in t = 2 and t = 5 for 'a' and 'b'

anonymous · Answer

Why is it that? I mean, why do you get s(b)-s(a)/(b-a) ?

anonymous · Answer

My math teacher said something about a timeline. Is there a way to use a timeline for this?

anonymous · Answer

IDK what you mean by timeline here
but the average of anything is the f(x2)-f(x1)/x2-x1 or the slope in other ways between two points one is final position and one is initial position

anonymous · Answer

the second part you need to take the derivative with respect to time and then evaluate at t=1 and at t=8

anonymous · Answer

Average velocity is given by the total change in position divided by the total change in time.