A Particle travels on the x-axis so its velocity at time t is given by v(t)=1/2-cos(t) meters per second, where t is between 0 and 2pi, inclusive.
A. For what values of t is the particle moving to the right?
B. If the particle starts at x=3, what is the final position of the article?
C. What is the total distance traveled by the particle?
D. When t=pi/4, is the speed of the particle increasing or decreasing?

Question

A Particle travels on the x-axis so its velocity at time t is given by v(t)=1/2-cos(t) meters per second, where t is between 0 and 2pi, inclusive. 
A. For what values of t is the particle moving to the right?
B. If the particle starts at x=3, what is the final position of the article?
C. What is the total distance traveled by the particle?
D. When t=pi/4, is the speed of the particle increasing or decreasing?

anonymous · Answer

particle moves right for + values of v. pi/3<t<5pi/3
x(t)=.5t-sint+c and x=3 for t=0. So c=3
the final position after 2pi seconds=pi+3
find the total distance by using a line graph separating the positive and negative velocities.
a(t)=sin(t); a(pi/4)=.5 therefore increasing