1. ## differenciation

A particle moves along a straight line and its position at time is given by where s is measured in feet and t in seconds.
Find the velocity (in ft/sec) of the particle at time :
The particle stops moving (i.e. is in a rest) twice, once when and again when where . is
and is
What is the position of the particle at time ?
Finally, what is the TOTAL distance the particle travels between time and time ? ........how do we find the total distance???????

2. Originally Posted by sss
A particle moves along a straight line and its position at time is given by where s is measured in feet and t in seconds.
Find the velocity (in ft/sec) of the particle at time :
you want s'(0)

the velocity function is the derivative of the position function
The particle stops moving (i.e. is in a rest) twice, once when and again when where . is
and is
you want to solve v(t) = s'(t) = 0

What is the position of the particle at time ?
s(18)

Finally, what is the TOTAL distance the particle travels between time and time ? ........how do we find the total distance???????
if you have learned integrals, this is $\int_0^{18} |v(t)|~dt$

3. Originally Posted by Jhevon
if you have learned integrals, this is $\int_0^{18} |v(t)|~dt$

...but what if you have not learned integrals; is there another way of approaching this problem?

4. Originally Posted by calculus shmalculus
...but what if you have not learned integrals; is there another way of approaching this problem?
total distance = [s(3) - s(0)] - [s(6) - s(3)] + [s(18) - s(6)]