Interpret r(t) as the position of a moving object at time t. find the curvature of the path and determine thetangential and normal components of acceleration .r(t) = cos 2t i + sin 2t j + k.

The curvature is

The tangential component of acceleration is

The normal component of acceleration is

Step-by-step explanation:

To find the curvature of the path we are going to use this formula:

where

is the unit tangent vector.

is the speed of the object

We need to find , we know that so

Next , we find the magnitude of derivative of the position vector

The unit tangent vector is defined by

We need to find the derivative of unit tangent vector

And the magnitude of the derivative of unit tangent vector is

The curvature is

The tangential component of acceleration is given by the formula

We know that and

so

The normal component of acceleration is given by the formula

We know that and so

good job you smart son of a gun you are smarter that einstein. 7