Question

A particle moves along the x-axis so that it’s position s in meters at any time t>0 in seconds is given by the function s(t)=2t+2sin((pi/2)t).

A. Find the velocity of the particle, and then determine the velocity at times t=1 and t=2.
B. Is the particle speeding up or slowing down at t=1.9 seconds? Justify your answer.
C. Find the time t on the interval [0,3] at which the particle is farthest to the right. Justify your answer.

Answer 1

v(t) = ds/dt = 2 + πcos(π/2 t)
so now answer A with t = 1,2
B. a(t) = dv/dt = -π^2/2 sin(π/2 t)
if a(1.9) < 0 then the velocity is decreasing
C. s(t) has a maximum when v(t) = 0 and a(t) < 0
but you already know that sin(x) has a max at x = π/2 -- that is, when t=1

Answer 2

whats c