Chapter 14.3, Problem 83E

Nonuniform straight-line motion Consider the motion of an object given by the position function

$r(t)=f(t)\langle a,b,c\rangle +\langle x_0,y_0,z_0\rangle ,\text{for}t\ge 0,$

where a, b, c, x₀, y₀, and z₀ are constants, and f is a differentiable scalar function, for t ≥ 0.

1. a. Explain why this function describes motion along a line.
2. b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?