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