Page 148 - Calculus Workbook For Dummies

132 Part III: Differentiation

Average velocity is defined as total displacement divided by total time. Say Glutius
completes the race in 1 hour. Because he traveled 200 palameters, his average
speed would be 200 palameters per hour. But because the total displacement is
only 100, his average velocity would be a mere 100 palameters per hour (roughly
7 miles per hour).
Speed is regular old speed, and, unlike velocity, it’s always positive (or zero). If
Maximus picks up speed to make the jump over the lion pit, his speed, naturally,
would be increasing. Note: His velocity would be decreasing — even though we
would see him speeding up — because his velocity would be negative and would
be becoming a larger and larger negative.
The meaning of acceleration, like velocity, (in calculus and physics) agrees with
the way we use it in everyday life only for movement to the right (or up). But,
going left (or down), it’s strange. When Glutius speeds up to jump over the lion
pit, we would say that he’s accelerating. But because his velocity is becoming a
larger and larger negative and is thus decreasing, he is technically decelerating.

9. For problems 9, 10, and 11, a duck-billed
platypus is swimming back and forth along
the side of your boat, blithely unaware that
he’s the subject for calculus problems in
rectilinear motion. The back of your boat is
at the zero position, and the front of your
boat is in the positive direction (see the fol-
lowing figure). s(t) gives his position (in
feet) as a function of time (seconds). Find
his a) position, b) velocity, c) speed, and d)
acceleration, at t = 2 seconds.
Solve It

0 +

2
s t = t 5 + 4
^ h