Question

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

Answer 1

sin(t)j - cos(t)i

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