Question

an object moves along the x axis with initial position x(0)=2. the velocity of the object at time t>=0 is given by v(t)=sin(pi/3 t). what is the acceleration of the object at time t=4?? please help and show steps!

Answer 1

v(t) = sin((pi/3)t)
a(t) = dv/dt = (pi/3)cos((pi/3)t)
When t = 4
a(4) = (pi/3)cos((pi/3).4) = (pi/3)cos(pi + pi/3) = -(pi/3)cos(pi/3)

I don't have a clue what you are talking about in (b). Can you sort it out?

s = Int{0 =>4(sin((pi/3)t)dt} = {-(3/pi)cos((pi/3)t)}[0 => 4]
s = -(3/pi){cos(4pi/3) - 1} = =-(3/pi){-cos(pi/3) - 1} = 3/(2.pi) + 3/pi = 9/(2.pi)