...My class is doing a test review for homework, and I was doing well so far until I bumped into this:
A particle moves along the x-axis in such a way that its acceleration at time t for t (greater than or equal to) 0 is given by a(t)=2 cos(t). At time t=0, the velocity of the particle is v(0)= -1 and its position is x(0)= 0.
a. Write an equation for the velocity for the velocity v(t) of the particle.
Already found this, it was: v(t)=2 sin t -1
b. Write an equation for the position x(t) of the particle.
Found this also, which was: x(t)= -2 cos t - t +2
c. For what values of t, 0< t < , is the particle at rest? (less thans are less than or equal to).
The problem I have with this is isolating t using: -1= -2 cos t - t +2
to find when the particle is at rest, set v(t) = 0, not x(t).
I already did a similar problem, but it was much simpler to isolate t to one side and solve for it. (2 -2 sin 2 t = 0 ----> t=0.25)
Another little question while I'm on the subject, how do I I'm too used to single terms.
chain rule ...