Question

Given an acceleration​ vector, initial velocity left angle u 0 comma v 0 right angle​, and initial position left angle x 0 comma y 0 right angle​, find the velocity and position vectors for tgreater than or equals0. a​(t)equalsleft angle 0 comma 12 right angle​, left angle u 0 comma v 0 right angleequalsleft angle 0 comma 6 right angle​, left angle x 0 comma y 0 right angleequalsleft angle 6 comma negative 1 right angle

Answer 1

For the velocity vector, we have

V(t) = dR

dt = (1, 2t, 3t

2

).

For the acceleration vector, we get

A =

dV

dt = (0, 2, 6t).

The velocity vector at t = 1 is

V(1) = (1, 2, 3).

The speed at t = 1 is

kV(1)k =

p

1

2 + 22 + 32 =

√

14.