96
Chapter 3Acceleration and Free Fall
6. A toy car is released on one side of a piece of track that is bent into an
upright U shape. The car goes back and forth. When the car reaches the
limit of its motion on one side, its velocity is zero. Is its acceleration also
zero. Explain using a v-t graph. [Based on a problem by Serway and
Faughn.]
7. What is the acceleration of a car that moves at a steady velocity of 100
km/h for 100 seconds. Explain your answer. [Based on a problem by
Hewitt.]
8. A physics homework question asks, "If you start from rest and accelerate
at 1.54 m/s
2
for 3.29 s, how far do you travel by the end of that time." A
student answers as follows:
1.54 x 3.29 = 5.07 m
His Aunt Wanda is good with numbers, but has never taken physics. She
doesn't know the formula for the distance traveled under constant accelera-
tion over a given amount of time, but she tells her nephew his answer
cannot be right. How does she know.
9 . You are looking into a deep well. It is dark, and you cannot see the
bottom. You want to find out how deep it is, so you drop a rock in, and you
hear a splash 3.0 seconds later. How deep is the well.
10. You take a trip in your spaceship to another star. Setting off, you
increase your speed at a constant acceleration. Once you get half-way there,
you start decelerating, at the same rate, so that by the time you get there,
you have slowed down to zero speed. You see the tourist attractions, and
then head home by the same method.
(a) Find a formula for the time, T, required for the round trip, in terms of d,
the distance from our sun to the star, and a, the magnitude of the accelera-
tion. Note that the acceleration is not constant over the whole trip, but the
trip can be broken up into constant-acceleration parts.
(b) The nearest star to the Earth (other than our own sun) is Proxima
Centauri, at a distance of d=4x10
16
m. Suppose you use an acceleration of
a=10 m/s
2
, just enough to compensate for the lack of true gravity and make
you feel comfortable. How long does the round trip take, in years.
(c) Using the same numbers for d and a, find your maximum speed.
Compare this to the speed of light, which is 3.0x10
8
m/s. (Later in this
course, you will learn that there are some new things going on in physics
when one gets close to the speed of light, and that it is impossible to exceed
the speed of light. For now, though, just use the simpler ideas you've
learned so far.)
11. You climb half-way up a tree, and drop a rock. Then you climb to the
top, and drop another rock. How many times greater is the velocity of the
second rock on impact. Explain. (The answer is not two times greater.)
12. Alice drops a rock off a cliff. Bubba shoots a gun straight down from the
edge of the same cliff. Compare the accelerations of the rock and the bullet
while they are on the way down. [Based on a problem by Serway and
Faughn.]