Answer
a. $10$ cm; $5$ cm; $-5\sqrt 2$ cm;
b. $0$ cm/s; $-5\sqrt 3$ cm/s; $-5\sqrt 2$ cm/s.
Work Step by Step
Given the motion equation $x=10cos(t)$, we have:
a. at $t=0$, $x_1=10cos(0)=10$ cm; at $t=\pi/3$, $x_2=10cos(\pi/3)=10/2=5$ cm; and $t=3\pi/4$, $x_3=10cos(3\pi/4)=-10\sqrt 2/2=-5\sqrt 2$ cm;
b. $v(t)=x'=-10sin(t)$, at $t=0$, $v_1=-10sin(0)=0$ cm/s; at $t=\pi/3$, $v_2=-10sin(\pi/3)=-5\sqrt 3$ cm/s; and $t=3\pi/4$, $v_3=-10sin(3\pi/4)=-5\sqrt 2$ cm/s.
