Expert: Paul Klarreich - 12/3/2009

Question
  Suppose a particle is observed moving along a straight line, and suppose  that the velocity v of the particle as a function of time t is given by v(t)=2sin⁡tπ (mm/s).
   a)Find the net change in the position of the particle in the first 3 seconds;
   b)Find the time t when the particle is at the rest in the first 3 seconds;
   c)Find the total distance travelled by the particle during the first 3 seconds.


Answer
Questioner: pankti
Country: Canada
Category: Calculus
Private: No
Subject: itegrals
Question: Suppose a particle is observed moving along a straight line, and suppose  that the velocity v of the particle as a function of time t is given by v(t)=2sin⁡tπ (mm/s).
a)Find the net change in the position of the particle in the first 3 seconds;
b)Find the time t when the particle is at the rest in the first 3 seconds;
c)Find the total distance travelled by the particle during the first 3 seconds.
.......................
I cannot read your function.  Do NOT use fancy symbols on this site.

BUT:

a. Net change is just  v(3) - v(0).

b. Find t where  v'(t) = 0.

c. This is an integral:

{ t=3
|      abs(v'(t)) dt
} t=0

That will require the results of part b.