Analyzing Parametric Motion: Defining, Constraining, and Interpreting Motion
Consider an object moving along a path defined by the position vector function \( \mathbf{r}(t) = \langle 3t – 2, \; t^2 – 4t + 5 \rangle \). Solve the following parts: (a) Define ‘motion’ in the context of parametric vector kinematics. Specifically, describe the roles of the position vector, velocity vector, and acceleration vector […]
Part b
Given the initial parametric equations \( x(t) = 3t – 2 \) and \( y(t) = t^2 – 4t + 5 \), modify the expression for \( x(t) \) so that the object’s speed remains constant at \(3\) units for \( t \geq 2 \). Assume that \(x(t)\) is continuous at \(t=2\).