A particle is moving in R 3 so that its acceleration function is a (...

Patricia Bean

Patricia Bean

Answered

2022-07-15

A particle is moving in R 3 so that its acceleration function is a ( t ) = 2 t , 1 , 0 . Find the position function, r(t) of the particle if it starts at the point ( 5 , 0 , 2 ) with initial velocity v ( t ) = 3 , 1 , 1
We have v ( t ) = 3 , 1 , 1 so r ( t ) = v ( t ) d t= 3 , 1 , 1 d t which is 3 t , t , t
From here I don't know what to do.

Answer & Explanation

lelapem

lelapem

Expert

2022-07-16Added 12 answers

Let
a ( t ) = 2 t , 1 , 0
According to the definition
d v d t = a
Integrating with respect to time
v ( t ) v ( 0 ) = 0 t a ( λ ) d λ
So we have
v ( t ) = 3 , 1 , 1 + t 2 , t , 0 = t 2 + 3 , t + 1 , 1
Similarly
r ( t ) r ( 0 ) = 0 t v ( λ ) d λ
And then
r ( t ) = 5 , 0 , 2 + t 3 / 3 + 3 t , t 2 / 2 + t , t = t 3 / 3 + 3 t 5 , t 2 / 2 + t , t + 2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?