An object moves along thex-axis with acceleration given by a(t) = sin 2t, t being the time, measured in seconds. At t = 0, its position is given by s = 5, and its velocity at t = 0 is v = −1/2 (that is, it is moving to the left at a speed of 1/2 unit per second).
(a) Where is it after 5 seconds?(c) What is the farthest right it gets, and when does it first get there?
(b) What is the farthest left it gets, and when does it first get there?
how would i start off by tacking this question.
do i need to integrate sin2t to get the velocity?
Hello, jvignacio!
We are given the acceleration function.An object moves along the x-axis with acceleration: . measured in seconds.
At , its position is and its velocity is
(a) Where is it after 5 seconds?
(b) What is the farthest left it gets, and when does it first get there?
(c) What is the farthest right it gets, and when does it first get there?
We must find the velocity function and the position function.
To find , integrate .[1]
We are told that: .
. . So we have: .
. . The velocity function is: .
To find , integrate
We are told that: .
. . So we have: .
. . The position function is: .
Now you are ready to answer the questions . . .