Question

Find the acceleration vector a(t) for the position vector r(t) = (sin(t), cos(t),t).

Answer 1

To find the acceleration vector a(t) for the given position vector, we need to take the second derivative of the position vector with respect to time. The acceleration vectors in each direction can be found by differentiating each component of the position vector twice.

Step-by-step explanation:

To find the acceleration vector a(t) for the given position vector r(t) = (sin(t), cos(t),t), we need to take the second derivative of the position vector with respect to time. The acceleration vectors in each direction can be found by differentiating each component of the position vector twice.

Given position vector: r(t) = (sin(t), cos(t),t)

Acceleration vector: a(t) = (d²/dt²(sin(t)), d²/dt²(cos(t)), d²/dt²(t))

Using the derivatives of sine and cosine functions, we find that a(t) = (-sin(t), -cos(t), 0).