Section 1.3 Extra Practice
STUDENT BOOK PAGES 22–31
1. The velocity of an object is given by
v(t) ⫽ 2t 2 ⫺ 4t ⫺ 6. At what time, in seconds, is
the object at rest? Explain why there are not two
times when the object is at rest.
2. What is the difference between velocity and speed?
3. For the following position function, calculate the
average velocity between the given time values.
f (t) ⫽ 兹t ⫺ 1
a. t ⫽ 1 and t ⫽ 5
b. t ⫽ 3 and t ⫽ 5
c. t ⫽ 5 and t ⫽ 10
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4. A person at the top of a large building decides to drop
a penny off the side of the building. Suppose that
after t seconds, the penny has fallen a distance of
s metres, where s(t) ⫽ 405 ⫺ 5t 2, 0 ⱕ t ⱕ 9.
a. Calculate the average velocity between 1 and
2 seconds.
b. Calculate the average velocity between 1 and
9 seconds.
c. Calculate the velocity at the time t ⫽ 1.
d. Calculate the velocity at the time t ⫽ 4.
5. Suppose that a foreign language student has learned
N(t) ⫽ 64t ⫺ t 3 vocabulary terms after t hours of
uninterrupted study.
a. How many terms have been learned at
time t ⫽ 3 h?
b. What is the rate that terms are learned between
time t ⫽ 1 h and t ⫽ 2 h?
c. What is the rate that terms are learned between
time t ⫽ 2 h and t ⫽ 3 h?
d. What is the rate in terms per hour at which the
student is learning at time t ⫽ 3 h?
f (x) ⫺ f (a)
to
x⫺a
x→a
6. Use the alternate definition lim
calculate the instantaneous rate of change of f (x) at
each of the given points.
a. f (x) ⫽ x 2; (1, 1)
b. f (x) ⫽ 兹x ⫺ 7; (11, 2)
1
c. f (x) ⫽ ; (1, 1)
x
7. Suppose the motion of an avalanche is described by
s(t) ⫽ 4t 2, where s is the distance in metres travelled
by the leading edge of the snow at t seconds.
a. Find the distance travelled from 3 s to 6 s.
b. Find the average rate at which the avalanche is
moving from 0 s to 12 s.
c. Find the rate at which the avalanche is moving
at 12 s.
d. How long, to the nearest second, does the leading
edge of the snow take to move 800 m?
8. A manufacturer of basketballs finds that the profit
from the sale of x basketballs per week is given by the
function P(x) ⫽ 180x ⫺ 2x 2, where P is measured in
dollars.
a. Find the profit on the sale of 60 basketballs.
b. What is the rate of change of profit between the
time of selling 20 basketballs and 60 basketballs?
c. Using a graphing calculator, graph the profit
function and, from the graph, determine for what
sales levels of x the rate of change of profit is
positive.
Section 1.3 Extra Practice
327