The position vector for particle A is cos (t) i, and the position vector for particle B is sin (t) j. What is the difference in acceleration (i. e. the relative acceleration) between particle A and B at any time t? The acceleration vector of a particle moving in space is the second derivative of the position vector

sin (t) j - cos (t) i

Step-by-step explanation:

Let's start with A:

Position vector = cos (t) i

Velocity vector = - sin (t) i (differentiating the position vector)

acceleration vector = - cos (t) i (differentiating the velocity vector)

Then we go to B:

Position vector = sin (t) j

Velocity vector = cos (t) j

acceleration vector = - sin (t) j

Relative acceleration = - cos (t) i - (-sin (t) j) = sin (t) j - cos (t) i