A Particle moves along the x axis so that at time t its position is given by x(t)=sin( pi t^2)
(A.)Find the Velocity at time t
(B.)Find the acceleration of time t
(C.)For What Value of t does the particle change direction
(D.)All Values of t that the particle is moving to the left
Hello, Dragon!
Velocity is the derivative of the position function.A particle moves along the x axis so that at time its position is given by: .
(A) Find the velocity at time
. .
Acceleration is the derivative of the velocity function.(B) Find the acceleration at time
. .
. . . . . .
Big hint: In order to change direction, the particle must come to a stop.(C) For what value of does the particle change direction?
. .
The question becomes: When is the velocity equal to zero?
We have: .
. .
. .
. . . . . . for any integer
This part is very messy ... I'm still working on it.(D) All values of that the particle is moving to the left.
If the particle is moving to the left, its velocity is negative.
We have: .
. . Good luck!