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

Question

Wyatt

Mathematics

7 September, 13:44

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

+1

Answers (1)

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Camren Allen · 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.