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Homework Problems
1 . The graph shows the motion of a car stuck in stop-and-go freeway
traffic. (a) If you only knew how far the car had gone during this entire
time period, what would you think its velocity was. (b) What is the car’s
maximum velocity.
2. (a) Let
.
be the latitude of a point on the Earth's surface. Derive an
algebra equation for the distance, L, traveled by that point during one
rotation of the Earth about its axis, i.e. over one day, expressed in terms of
L,
.
, and R, the radius of the earth. Check: Your equation should give L=0
for the North Pole.
(b) At what speed is Fullerton, at latitude
.
=34
°
, moving with the
rotation of the Earth about its axis. Give your answer in units of mi/h. [See
the table in the back of the book for the relevant data.]
3. A person is parachute jumping. During the time between when she
leaps out of the plane and when she opens her chute, her altitude is given by
the equation
y=(10000 m) - (50 m/s)[t+(5.0 s)
e
-t/5.0 s
] .
Find her velocity at t=7.0 s. (This can be done on a calculator, without
knowing calculus.) Because of air resistance, her velocity does not increase
at a steady rate as it would for an object falling in vacuum.
4 S. A light-year is a unit of distance used in astronomy, and defined as the
distance light travels in one year. The speed of light is 3.0x10
8
m/s. Find
how many meters there are in one light-year, expressing your answer in
scientific notation.
5 S. You’re standing in a freight train, and have no way to see out. If you
have to lean to stay on your feet, what, if anything, does that tell you about
the train’s velocity. Its acceleration. Explain.
6
.
. A honeybee’s position as a function of time is given by x=10t-t
3
, where t
is in seconds and x in meters. What is its velocity at t=3.0 s.
7 S. The figure shows the motion of a point on the rim of a rolling wheel.
(The shape is called a cycloid.) Suppose bug A is riding on the rim of the
wheel on a bicycle that is rolling, while bug B is on the spinning wheel of a
bike that is sitting upside down on the floor. Bug A is moving along a
cycloid, while bug B is moving in a circle. Both wheels are doing the same
number of revolutions per minute. Which bug has a harder time holding
on, or do they find it equally difficult.
8 . Peanut plants fold up their leaves at night. Estimate the top speed of
the tip of one of the leaves shown in the figure, expressing your result in
scientific notation in SI units.
Problem 1.
SA solution is given in the back of the book.A difficult problem.
A computerized answer check is available.
.
A problem that requires calculus.
04812
time (s)
0
10
20
30
40
50
60
70
80
90
distance
(m)
Problem 7.
Problem 8.
Chapter 2Velocity and Relative Motion