The position vector r describes the path of an object moving in the xy-plane. position vector point r(t) = ti + (ât2 + 7)j (1, 6) (a) find the velocity vector, speed, and acceleration vector of the object.
The position vector decomposed is: [tex]r_x = t[/tex] [tex]r_y = at^2 + 7[/tex]
The velocity vector can be found computing the derivative of r on both axes: [tex]r'_x = 1[/tex] [tex]r'_y=2at[/tex] So, the velocity vector is r' = 1i+2atj
The speed (the magnitude of the velocity vector) is [tex]v= \sqrt{(1)^2+(2at)^2} [/tex] Finally we can write the acceleraion vector by performing derivation on the velocity vector: [tex]r''_x=0[/tex] [tex]r''_y=2a[/tex] and so r''=2a j
