Given Position Measurements, How to Estimate Velocity and Acceleration

1. How do you find the velocity vector from a position vector?
2. What is the mathematical relationship between position velocity acceleration and time?

How do you find the velocity vector from a position vector?

For vector calculus, we make the same definition. Let r(t) be a differentiable vector valued function representing the position vector of a particle at time t. Then the velocity vector is the derivative of the position vector. v(t)=r′(t)=x′(t)ˆi+y′(t)ˆj+z′(t)ˆk.

What is the mathematical relationship between position velocity acceleration and time?

Velocity is directly proportional to time when acceleration is constant (v ∝ t). Displacement is proportional to time squared when acceleration is constant (∆s ∝ t²).