Physics Chapter 3
"She moves at a constant speed in a constant direction." Rephrase the same sentence in fewer words.
"She moves at a constant velocity."
What is the acceleration of a car that maintains a constant velocity of 100 km/h for 10 s? (Why do some of your classmates who correctly answer the preceding question get this question wrong?)
0 km/h·s
What is the acceleration of a car moving along a straight road that increases its speed from 0 to 100 km/h in 10 s?
10 km/h·s
Consider these measurements: 10 m, 10 m/s, and 10 m/s2. Which is a measure of speed, which of distance, and which of acceleration?
10 m is distance, 10 m/s is speed, and 10 m/s2 is acceleration.
How far does a horse travel if it gallops at an average speed of 25 km/h for 30 min?
12 km
What is the speed over the ground of an airplane flying at 100 km/h relative to the air caught in a 100-km/h right-angle crosswind?
141 km/h
What is the average speed in kilometers per hour of a horse that gallops a distance of 15 km in a time of 30 min?
30 km/hr
When are you most aware of your motion in a moving vehicle: when it is moving steadily in a straight line or when it is accelerating? If you were in a car that moved with absolutely constant velocity (no bumps at all), would you be aware of motion?
Accelerating. You would not be aware of the motion if you did not look outside the car.
What is the effect of air resistance on the acceleration of falling objects?
Air resistance decreases the acceleration of falling objects.
What exactly is meant by a "freely falling" object?
An object in free fall falls under gravity alone with no friction.
The speedometer of a car moving to the east reads 100 km/h. The car passes another car that is moving to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?
Both cars have the same speed, but they have opposite velocities because they are moving in opposite directions.
Which undergoes greater acceleration: an airplane that goes from 1000 km/h to 1005 km/h in 10 seconds or a skateboard that goes from zero to 5 km/h in 1 second?
Both gain 5 km/h, but the skateboard does so in one-tenth the time. The skateboard therefore has the greater acceleration—in fact, ten times greater. A little figuring will show that the acceleration of the airplane is 0.5 km/h·s, whereas the acceleration of the slower-moving skateboard is 5 km/h·s. Velocity and acceleration are very different concepts. Distinguishing between them is very important.
What two units of measurement are necessary for describing speed?
Distance and time
What relationship between distance traveled and time did Galileo discover for freely falling objects released from rest?
Galileo discovered that distance increased as the time squared.
What is the distance fallen for a freely falling object 1 s after being dropped from a rest position? What is the distance for a 4-s drop?
It falls 5 m in 1 s and 80 m in 4 s.
What is the gain in speed per second for a freely falling object?
It gains approximately 10 m/s.
When an object is thrown upward, how much speed does it lose each second (ignoring air resistance)?
It loses 10 m/s of speed each second until it reaches the high point, then it gains 10 m/s each second.
If a car is moving at 90 km/h and it rounds a corner, also at 90 km/h, does it maintain a constant speed? A constant velocity? Defend your answers.
It maintains a constant speed, but does not maintain a constant velocity.
Would it be possible to attain this average speed and never go faster than 80 km/h?
No, not if the trip starts from rest. There are times in which the instantaneous speeds are less than 80 km/h, so the driver must drive at speeds higher than 80 km/h during one or more time intervals in order to average 80 km/h. In practice, average speeds are usually much lower than highest instantaneous speeds.
average speed
Path distance divided by time interval total distance covered/ time interval
A particular car can go from rest to 90 km/h in 10 s. What is its acceleration?
The acceleration is 9 km/h·s. Strictly speaking, this would be its average acceleration because there may have been some variation in its rate of picking up speed.
What did Galileo discover about the amount of speed a ball gained each second when rolling down an inclined plane? What did this say about the ball's acceleration?
The ball had constant acceleration, so it gained the same speed every second.
During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity?
The constant speedometer reading indicates a constant speed but not a constant velocity, because the car may not be moving along a straightline path, in which case it is accelerating.
If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km. a. How far would it travel if it moved at this rate for 4 h? b. For 10 h?
The distance traveled is the average speed × time of travel, so a. Distance = 60 km/h × 4 h = 240 km b. Distance = 60 km/h × 10 h = 600 km
A hungry mosquito sees you resting in a hammock in a 3-m/s breeze. How fast and in what direction should the mosquito fly in order to hover above you for lunch?
The mosquito should fly toward you into the breeze. When just above you, it should fly at 3 m/s in order to hover at rest. Unless its grip on your skin is strong enough after landing, it must continue flying at 3 m/s to keep from being blown off. That's why a breeze is an effective deterrent to mosquito bites.
The acceleration of free fall is about 10 m/s2. Why does the seconds unit appear twice?
The second appears once in the denominator of the unit for speed and once for the interval of time.
What is the speed acquired by a freely falling object 5 s after being dropped from a rest position? What is the speed 6 s after?
The speed is 50 m/s after 5 s and 60 m/s after 6 s.
What relationship did Galileo discover about a ball's acceleration and the steepness of an incline? What acceleration occurs when the plane is vertical?
The steeper the incline, the greater the acceleration. On a vertical incline, the ball is in free fall.
What is the main difference between speed and velocity?
Velocity includes a direction, but speed does not.
Acceleration is generally defined as the time rate of change of velocity. When can it be defined as the time rate of change of speed?
When moving in a straight line, the time rate of change of speed is acceleration.
Consider a motorboat that normally travels at 10 km/h in still water. If the boat heads directly across the river, which also flows at a rate of 10 km/h, what will be its velocity relative to the shore?
When the boat heads cross-stream (at a right angle to the river flow), its velocity is 14.1 km/h, 45° downstream. Recall from Chapter 2 that the parallelogram formed by a pair of equal-length vectors at right angles to each other is a square that has a diagonal √2 times the length of each side (see Figure 2.9)
If a car moves with a constant velocity, does it also move with a constant speed?
Yes, because constant velocity requires constant speed in the same direction.
As you read this in your chair, how fast are you moving relative to the chair? Relative to the Sun?
You are not moving relative to the chair, but you are moving over 100,000 km/h relative to the Sun.
What is the acceleration of a race car that whizzes past you at a constant velocity of 400 km/h?
Zero, because its velocity doesn't change.
vector quntity
a quantity in physics that has both magnitude and direction
scalar quantity
a quantity in physics, such as mass, volume and time that can be completely specified by its magnitude and has no direction
In 2.5 s, a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h. Which undergoes the greater acceleration? What is the acceleration of each?
acceleration = change in velocity / change in time = 65 km/h - 60 km/h / 2.5s = 5km/h / 2.5s = 2 km/hs
velocity acquired =
acceleration x time
What is the average speed of a cheetah that sprints 100 meters in 4 seconds? If it sprints 50 m in 2 s?
average speed = distance covered / time interval = 100 meters / 4 seconds = 50 meters / 2 seconds = 25 m/s
In addition to the speedometer on the dashboard of every car is an odometer, which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one-half hour later, what has been your average speed?
average speed = total distance covered / time interval = 40 km / 0.5 h = 80 km/h
total distance covered =
average speed x time interval
Speed
how fast something moves, the distance an object travels per unit of time; the magnitude of velocity distance/time
What kind of speed is registered by an automobile speedometer: average speed or instantaneous speed?
instantaneous speed
free fall
motion under the influence of gravity only
acceleration
the rate at which an object's velocity changes with time; the change in velocity may be in magnitude (speed), or direction, or both change in velocity / time interval
Instantaneous speed
the speed at an instant
velocity
the speed of an object and its direction of motion; a _______ quantity.