Question

For the given position vectors, compute the tangent velocity vector for the given value of t?

Answer 1

To compute the tangent velocity vector, you need to take the derivative of the position vector with respect to time.

Step-by-step explanation:

The tangent velocity vector can be computed by taking the derivative of the position vector with respect to time. In the given position function, ř(t) = 2.0t²î + (2.0 + 3.0t)ĵ + 5.0tkm, the derivative will give us the velocity function v(t).

The derivative of each component of ř(t) gives us:

x(t) = 4.0tî

y(t) = 3.0ĵ

z(t) = 5.0k

Therefore, the tangent velocity vector at any time t can be written as:

v(t) = 4.0tî + 3.0ĵ + 5.0k m/s