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## Homework Statement

Find the velocity and acceleration vectors for the following curves. Determine the points where the velocity vector is changing DIRECTION but not changing SPEED,

and the points where the velocity vector is changing SPEED but not DIRECTION.

For:

a. f(t) = (t,t

^{2},t

^{3})

b. (e

^{-t}, e

^{2t})

## Homework Equations

If we want to change the speed but not direction, the acceleration vector must be parallel to the velocity vector.

If we want to change the direction but not the speed, the acceleration vector should be perpendicular to the velocity vector.

## The Attempt at a Solution

Ok so here I go.

I will attempt to change the speed but not direction, so I need to do v=ka, and solve for k and then solve for t to get the points, correct?

And if I want to change the direction but not the speed, how should I find the points?

Thanks again, everyone.