Chapter 2 Problems
1,
2
,
3
= straightforward, intermediate,
challenging
Section 2.1
Position,
Velocity, and Speed
1.
The position of a pinewood derby
car was observed at various times; the
results are summarized in the following
table. Find the average velocity of the car
for (a) the first second, (b) the last 3 s, and
(c) the entire period of observation.
t
(s)
0
1.0
2.0
3.0
4.0
5.0
x
(m)
0
2.3
9.2
20.7
36.8
57.5
2.
(a)
Sand dunes in a desert move over
time as sand is swept up the windward side
to settle in the lee side.
Such “walking”
dunes have been known to walk 20 feet in a
year and can travel as much as 100 feet per
year in particularly windy times.
Calculate
the average speed in each case in m/s. (b)
Fingernails grow at the rate of drifting
continents, on the order of 10 mm/yr.
Approximately how long did it take for
North America to separate from Europe, a
distance of about 3 000 mi?
3
.
The position versus time for a certain
particle moving along the
x
axis is shown in
Figure P2.3. Find the average velocity in the
time intervals (a) 0 to 2 s, (b) 0 to 4 s, (c) 2 s
to 4 s, (d) 4 s to 7 s, (e) 0 to 8 s.
Figure P2.3
Problems 3 and 9
4.
A particle moves according to the
equation
x
= 10
t
2
where
x
is in meters and
t
is in seconds.
(a) Find the average velocity
for the time interval from 2.00 s to 3.00 s.
(b) Find the average velocity for the time
interval from 2.00 to 2.10 s.
5.
A person walks first at a constant
speed of 5.00 m/s along a straight line from
point
A
to point
B
and then back along the
line from
B
to
A
at a constant speed of
3.00 m/s. What is (a) her average speed over
the entire trip? (b) her average velocity over
the entire trip?
Section 2.2
Instantaneous Velocity and
Speed
6.
The position of a particle moving
along the
x
axis varies in time according to
the expression
x
= 3
t
2
, where
x
is in meters
and
t
is in seconds. Evaluate its position (a)
at
t
= 3.00 s and (b) at
3.00 s +
∆
t.
(c)
Evaluate the limit of
∆
x
/
∆
t
as
∆
t
approaches
zero, to find the velocity at
t
= 3.00 s.
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7
.
A positiontime graph for a particle
moving along the
x
axis is shown in Figure
P2.7. (a) Find the average velocity in the
time interval
t
= 1.50 s to
t
= 4.00 s. (b)
Determine the instantaneous velocity at
t
= 2.00 s by measuring the slope of the
tangent line shown in the graph. (c) At
what value of
t
is the velocity zero?
Figure P2.7
8
.
(a) Use the data in Problem 1 to
construct a smooth graph of position versus
time. (b) By constructing tangents to the
x
(
t
)
curve, find the instantaneous velocity of the
car at several instants. (c) Plot the
instantaneous velocity versus time and,
from this, determine the average
acceleration of the car. (d) What was the
initial velocity of the car?
9
.
Find the instantaneous velocity of
the particle described in Figure P2.3 at the
following times: (a)
t
= 1.0 s, (b)
t
= 3.0 s, (c)
t
= 4.5 s, and (d)
t
= 7.5 s.
10.
A hare and a tortoise compete in a
race over a course 1.00 km long. The
tortoise crawls straight and steadily at its
maximum speed of 0.200 m/s toward the
finish line. The hare runs at its maximum
speed of 8.00 m/s toward the goal for
0.800 km and then stops to tease the
tortoise. How close to the goal can the hare
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 Spring '08
 Entire
 Physics, Acceleration, Velocity

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