Randall D. Knight — Vectors and Coordinate Systems: Problem 23

The position of a particle as a function of time is given by \(\vec{r} = (3.0\hat{i} + 8.0\hat{j})t^2 \text{ m}\), where \(t\) is in seconds. a. What is the particle’s distance from the origin at \(t = 0, 2, \text{ and } 5 \text{ s}\)? b. Find an expression for the particle’s velocity \(\vec{v}\) as a function of time. c. What is the particle’s speed at \(t = 0, 2, \text{ and } 5 \text{ s}\)?