The position of a particular particle as a function of time is given by r = ( 9.60ti^ + 8.85j^ - 1.00t^2k^)m, where t is in seconds. Determine the particle's velocity 'v' as a function of time. "press your answer in terms of the unit vectors i, j, and k. Determine the particle's acceleration a as a function of time. Express your answer in terms of the unit vectors i, j, and k.

The velocity of an object is the variation of the object´s position over time. Then, the velocity can be expressed as the derivative of the position function:

v = dr / dt

Where

v = velocity

dr/dt = variation of the position over time

In this case, we have an object moving in a three-dimension system, that is, the direction of the moving object has an x, y, and z-component.

To obtain the components of the velocity vector, we have to derivate the components of the position vector with respect to time:

r = (9.60 · t i + 8.85 j - 1.00 · t² k)m

v = dr/dt = (9.60 i + 0 j - 2.00 · t k) m/s

The acceleration is the variation of velocity over time, then:

dv/dt = acceleration.

In this case, we have to derivate the velocity vector to obtain the acceleration vector:

a = dv/dt = (0 i + 0 j - 2.00 k) m/s²

The object is only accelerated in the z-direction and the acceleration is constant (-2 m/s²).