Question

The equation r(t)=(8 sin t) i+(8 cos t) j+(8t) k is the position of a particle in space at time t. Find the​ particle's velocity and acceleration vectors. Then write the​ particle's velocity at t= 3π 2 as a product of its speed and direction.

Answer 1

Velocity is
`8√(2)` and Acceleration is 8

Explanation:

Equation of position of the particle

r(t) = (8sint)i + (8cost)j + (8t)k

1) Velocity of the particle is
`(dr)/(dt)`

V(t) = dr/dt = (8cost)i + (-8sint)j + 8k

2) Acceleration of the particle will be
`(dv)/(dt)`

A(t) = dv/dt = (-8sint)i + (-8cost)j + 0k

velocity of the particle at t=
`(3pi)/(2)`

V(
`(3pi)/(2)`) = (0)i + (8)j + 8k =
`√(8^2+8^2)` =
`8√(2)`

acceleration at t=
`(3pi)/(2)`

A(
`(3pi)/(2)`) = (8)i + (0)j +0k =
`√(8^2)` = 8