Question

Найдите скоростьv (tо) и ускорение а(to) в момент to

1- s (t)=3cos2t, to=П/3
2- s (t)=2sin3t, to=П/4

Answer 1

$1)\; \; S(t)=3cos2t,\; t_0=\frac{\pi}{3}\\\\V(t)=S'(t)=-6sin2t,\; V(\frac{\pi}{3})=-6sin\frac{2\pi}{3}=-6\cdot \frac{\sqrt3}{2}=-3\sqrt3\\\\a(t)=V'(t)=-12\cdot cos2t,\; a(\frac{\pi}{3})=-12\cdot cos\frac{2\pi}{3}=-12\cdot (-\frac{1}{2})=6\\\\2)\; S=2sin3t,\; t_0=\frac{\pi}{4}\\\\V(t)=6cos3t,\; V(\frac{\pi}{4})=6cos\frac{3\pi}{4}=6\cdot (-\frac{\sqrt2}{2})=-3\sqrt2\\\\a(t)=-18sin3t,\; a(\frac{\pi}{4})=-18\cdot sin\frac{3\pi}{4}=-18\cdot \frac{\sqrt2}{2}=-9\sqrt2$