Answer
a. Velocity Vector: $3i+j$
Speed:$\sqrt 10$
Acceleration Vector: $0i+0j$
b. Velocity Vector: $3i+j$
Acceleration Vector: $0i+0j$
Work Step by Step
Position Vector: $r(t)=3ti+(t-1)j$
Point: (3,0)
a. Velocity Vector: $r'(t)=v(t)=3i+j$
Speed: Magnitude of Velocity Vector: $\sqrt ((f(t)i)^{2}+(g(t)j)^2)$
$=\sqrt ((3)^2+(1)^2)$=$\sqrt (9+1)=\sqrt 10$
Acceleration Vector: $r''(t)=v'(t)=0i+0j=0$
b. Plug in Given Values into Vectors
Velocity Vector: $3i+j$
Acceleration Vector: $0$
As the two vectors do not have any t values, they remain the same at all points.
