Let s = s(t) be the position function of a particle moving in a straight line.
Suppose that the position of the particle is given by the formula
s (t) = t^2 e^-t ; t >= 0
where t is measured in seconds and s in meters.
(i) Find the velocity of the particle at time t.
* should i differentiate s(t) to get the velocity?
(ii) When is the particle at rest?
* when velocity = 0.. am i right?
(iii) Find the total distance traveled by the particle during the first two seconds.
*dont have any idea..
(i) Find the velocity of the particle at time t.
* should i differentiate s(t) to get the velocity?
answer--> (2t e^-t) - (t^2 e^-t)
(ii) When is the particle at rest?
* when velocity = 0.. am i right?
answer-->
(2t e^-t) - (t^2 e^-t) = 0
(2t e^-t) = (t^2 e^-t)
(2e^-t) = (t e^-t)
*how to solve t?
(iii) Find the total distance traveled by the particle during the first two seconds.
*dont have any idea..
at t = 2
s (t) = t^2 e^-t
s (2) = 2^2 e^-2
.......= 0.54 meters
is my answer for (i) and (iii) is correct?
how am i going to solve (ii)?