Question

If the position function in feet of a particle at t seconds is s(t)=-16t^3+100t, find the following.

The average velocity of the particle from t=0 to t=2 seconds is...?

Answer 1

take the derivative of s(t), which is:
s(t)'=v(t)=-48t^2+100 <--- this is the equation for the velocity of the particle

to find the average velocity you have to find the integral of v(t)=-48t^2+100 from 0 to 2 and that will be your average velocity..

Answer 2

We haven't learned integrals yet.

Answer 3

Can you define what an integral is?

Answer 4

okay that's gonna be tough on here. all you have to do is then take v(t)=-48t^2+100, plug in 0 for t, that will be your first velocity, plug in 2 for t and that will be your second velocity. Take those 2 t's and divide by 2 to find the average velocity

Answer 5

i get 4 ft /sec...but the answer's 36 ft/sec

Answer 6

average velocity is defined as (change in position)/(change in time)...

Answer 7

^this guy's got it

Answer 8

I don't have position.

Answer 9

All i have is time and the function.

Answer 10

you have the equation to find position
just plug in 0 and 2 for time and you'll get the positions for those times

Answer 11

avg vel... = \(\large \frac{s(2)-s(0)}{2-0} \)

Answer 12

oh i see. so for that i just use the original function and substitute instead of deriving...If i derive and then substitute it'll give me instantaneous velocity. correct?

Answer 13

correct

Answer 14

Thanks!

Answer 15

Welcome