The equation bold r (t )equals(8 t plus 9 )bold i plus (2 t squared minus 8 )bold j plus (6 t )bold 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 equals 0 as a product of its speed and direction.

Explanation:

It is given that, the position of a particle as as function of time t is given by :

Let v is the velocity of the particle. Velocity of an object is given by :

So, the above equation is the velocity vector.

Let a is the acceleration of the particle. Acceleration of an object is given by :

At t = 0,

Hence, this is the required solution.