FIGURE N4–18
(e) For the speed |v| at any time tWe see immediately that the speed is a maximum when and a minimum when t = 0 or
π. The particle goes fastest at the ends of the minor axis and most slowly at the ends of the major
axis. Generally one can determine maximum or minimum speed by finding setting it equal to
zero, and applying the usual tests to sort out values of t that yield maximum or minimum speeds.
EXAMPLE 29
A particle moves along the parabola y = x^2 − x with constant speed Find v at (2,2).
SOLUTION: Since
and
Relation (3) holds at all times; specifically, at (2, 2), so that vx = ±1. From (1), then,
we see that vy = ±3. Therefore v at (2, 2) is either The former corresponds to
counterclockwise motion along the parabola, as shown in Figure N4–19a; the latter to clockwise
motion, indicated in Figure N4–19b.