Link to "Concepts and Skills"
 

motion diagram: A tool for the study of motion that uses a series of images to show the position of a moving object after equal time intervals

operational definition: Defines a concept in terms of the procedure or operation used

particle model: A simplified version of a motion diagram in which the object in motion is replace by a series of single points

coordinate system: A system used to describe motion that indicates where the zero point of the variable being studied is located and the direction in which the values of the variable increase

origin: The point in a coordinate system at which the variables have zero value

position vector: The arrow on a motion diagram that is drawn from the origin to the moving object 

scalar quantity: A quantity that only has magnitude

vector quantity: A quantity that has both magnitude and a direction

time (clock time): The time registered or showing on a clock being used to keep track of time

time interval: The duration of an event found by subtracting two clock times as in T(final) - T(initial) 

distance: A scalar quantity that measures the shortest length between two points

displacement: The vector quantity that defines the distance and the direction between two positions

speed: A scalar quantity that is derived by dividing the total distance traveled by the time interval during which it travelled the distance

velocity: A vector quantity derived by dividing the displacement of an object by the time interval over which the displacement occurs

instantaneous velocity: A single velocity measurement observed at a single moment in time, expressed as a clock time

average velocity: The sum of two or more velocity measurments divided by the number of velocity measurements used in calculating the sum 

instantaneous acceleration: A single acceleration measurement observed at a single moment in time, expressed as a clock time

average acceleration: The sum of two or more acceleration measurments divided by the number of acceleration measurements used in calculating the sum

final velocity: The observed (measured) velocity ar the end of a period of time over which a moving object is being observed

initial velocity:  The observed (measured) velocity ar the beginning of a period of time over which a moving object is being observed

uniform motion: Motion where equal displacenments occur during successive equal time intervals; Also referred to as a constant velocity scenario

acceleration due to gravity: (hisorical definition) The acceleration of an object in free fall resulting from earth's gravity; (general definition) The natural force of attraction between any two massive bodies, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. 

kinematics: The study of motion through the use of mathematics; the branch of mechanics concerned with motion without reference to force or mass

d = distance
d = displacement (in handwritten form an arrow is most often placed above the letter d; also d(i) = initial position and d(f) = final position)
v(ave) = average velocity (in hand written form a bar is most often placed over the v; also may be used to represent speed)
v(i) = initial velocity
v(f) = final velocity
a = acceleration
t = time (/\t often is used for the representation of a time interval though as often t will suffice)

v(f) = v(i) + at (this is the eqation that give us a = [v(f) - v(i)] / t]
d(f) = d(i) + (1/2) [v(i) + v(f)] t (often, but not always, d(i) = 0 units position)
d(f) = d(i) + v(i) t + (1/2) a t^2
v(f)^2 = V(i)^2 + 2 a [d(f) - d(i)]
 

Chapter 3
Reviewing Concepts

Questions:
Section 3.1
1. What is the purpose of drawing a motion diagram?
2. Under what circumstances is it legitimate to treat an object as a point particle?

Section 3.2
3. How does a vector quantity differ from a scalar quantity?
4. The following quantities describe location or its change: position, distance, and displacement.  Which are vectors?
5. How can you use a clock to find a time interval?

Section 3.3
6. What is the difference between average velocity and average speed?
7. How are velocity and acceleration relate?
8. What are the three parts of the problem solving strategy used in this book?
9. In which part of the problem solving strategy do you sketch the situation?
10. In which part of the problem solving strategy do you draw a motion diagram?

Chapter 3
Applying Concepts

Questions

11. Test the following combinations and explain why each does not have the properties needed to describe the concept of velocity: ?d + ?t, ?d - ?t, ?d * ?t, ?t/?d
12. When can a football be considered a point particle?
13. When can a football player be treated as a point particle?
14. When you enter a toll road, your toll ticket is stamped 1:00P.M. When you leave, after traveling 55 miles, your ticket is stamped 2:00P.M. What was your average speed in miles per hour?  Could you ever have gone faster than the average speed? Explain.
15. Does a car that's slowing down always have a negative acceleration?  Explain.
16. A croquet ball, after being hit by a mallet, slows down and stops.  Do the velocity and acceleration of the ball have the same signs?

Reminder:
Problem Solving Format:  If a problem solving format, which is a formal way of writing out the solutions to word problems, has not been introduced yet, it is suggested that you use an organized approach that includes the following five steps. In "multiple question" problems where more than one variable is being solved for, use multiple Equation, Substitution and Answer steps.

 1. Given: A statement of the given information.
 2. Find: A statement of exactly what you are being asked to find.
 3. Equation: A statement of the equation(s) to be used to find the answer(s).
 4. Substitution: A statement showing the substiturion into the eaution(s) with proper units.
 5. Answer: A statement of the answer(s) with appropriate units.
 

Problem Set #3:  Follow the written directions unless indicated otherwise by your instructor.

AVERAGE SPEED and VELOCITY:   v(ave) = d / t

1.  A boy walks 13 km in 2.0 h.  What is his speed in km/h and m/s?

2.  A high school athlete runs 1.00 x 10^2 m in 12.20 s.  What is her speed in m/s and km/h?

3.  A bullet is shot from a rifle with a speed of 720.0 m/s, E.
 a. What time is required for the bullet to strike a target 3240.0 m to the east?
 b. What is the velocity of the bullet in km/h?

4.  A rocket launched into outer space travels 240,000 km during the first 6.0 h after the 
 launching.  What is the average speed of the rocket in km/h and m/s?

5.  Light from the sun reaches earth in 8.3 min.  The speed of light is 3.00 x 10^8 m/s.  How
     far is the earth from the sun?

6.  On a baseball diamond, the distance from home plate to the pitcher's mound is 18.5m.  If a pitcher is capable of throwing a ball at 38.5 m/s, how much time does it take a thrown ball to reach home plate?

7.  A car is driven 60 km west in 40 min and then 70 km east in 50 min.  what is the average  speed and average velocity of the car in km/h?

8.  The French train in a sample problem is traveling 301 km/h.  When it is 360m from a road crossing, the engineer blows the whistle.  If the speed of sound is 330 m/s, how many seconds after the whistle is heard at the crossing will the train cross there?  [Hint: "time difference"]

ACCELERATION:  a = (vf - vi) / t

9.  What is the acceleration of a racing car if its velocity is increased uniformly from 44 m/s, S, to 66 m/s, S, over an 11-s period?

10.  What is the acceleration of a racing car moving south if its velocity is decreased uniformly from 66 m/s to 44 m/s over an 11-s period?

11.  A train moving west at a velocity of 15 m/s is accelerated uniformly to 17 m/s over a 12-s period.  What is its acceleration?

12.  A plane starting from rest (Vi = 0) is accelerated uniformly to its takeoff velocity of +72 m/s during a 5.0-s period.  What is the plane's acceleration?

13.  In a vacuum tube, an electron is accelerated uniformly from rest to a velocity of + 2.6 x
10^5 m/s during a time period of 6.5x10^-7 s.  Calculate the acceleration of the electron.

FINAL VELOCITY AFTER UNIFORM ACCELERATION:  vf = vi + a t

14.  A car is uniformly accelerated at the rate of +1.2 m/s^2 for 12 s.  If the original velocity of the car is +8.0 m/s, what is its final speed?

15.  An airplane flying at 90 m/s, E, is accelerated uniformly at the rate of 0.50 m/s^2, E, for 10.0s. What is its final velocity in m/s and km/h?

16a.  A race car traveling at 45 m/s east is slowed uniformly at the rate of -1.5 m/s^2 for 9.8 seconds. What is its final velocity in m/s?

16b. A spacecraft traveling at a speed of +1,210 m/s is uniformly accelerated at the rate of -150 m/s^2.  If acceleration lasts for 1.8 seconds, what is the final speed of the craft?
 

DISPLACEMENT DURING UNIFORM ACCELERATION:  d = [(vf + vi) / 2] t

17.  A race car starts from rest (Vi = 0) and is accelerated uniformly to +40 m/s in 8.0 seconds. What distance does the car travel?

18.  A race car traveling south at 44 m/s is uniformly decelerated to a velocity of 22 m/s, S, over an 11-s interval.  What is its displacement during this time?

19.  A rocket traveling at +88 m/s is accelerated uniformly to +132 m/s over a 15-s interval. What distance in meters does the rocket travel during this time?

20.  An engineer is to design a runway to accommodate airplanes that must gain ground speed of  60 m/s before they can take off.  These planes are capable of being accelerated uniformly at the rate of  +1.5 m/s^2.
 a.  How long will it take them to achieve takeoff speed?
 b.  What must be the minimum length of the runway?

CALCULATING DISPLACEMENT FROM ACCELERATION AND TIME:  d = vi t + 0.5 a t^2

21.  An airplane starts from rest and undergoes a uniform acceleration of +3.0 m/s^2 for 30.0 s before leaving the ground.  What is its displacement during the 30.0 s?

22.  A jet plane traveling at 88 m/s, N, lands on a runway and is decelerated uniformly to rest in 11s.
 a.  Calculate its acceleration.
 b.  Calculate the distance it travels.

23.  The Tokyo Express is uniformly accelerated from rest at +1.0 m/s^2 for 1.0 min.  How far does it travel during this time?

24.  Starting from rest, a racing car has displacement of 201m, S, in the first 5.0 s of uniform acceleration.  What is the car's acceleration?

25.  In an emergency, a driver brings a car to a full stop in 8.0s.  The car is traveling at a rate of +21 m/s when braking begins.
 a.  What is the car's acceleration?
 b.  How far does it travel before stopping?

26.  A stone is dropped from an airplane at a height of 490m.  The stone required 10.0s to reach the ground.  At what rate does gravity accelerate the stone? (assume downward is negative)

27.  A bicyclist approaches the crest of a hill at +4.5 m/s.  She accelerates down the hill at a rate of +0.40 m/s^2 for 12s.  How far does she move down the hill during this time interval?

CALCULATING ACCELERATION FROM DISPLACEMENT AND VELOCITY:
 a = (vf^2 - vi^2) / 2d             vf^2 = v^i2 + 2ad  d = (vf^2 - vi^2) / 2a

28.  A plane is accelerated from a speed of 2.0 m/s at the constant rate of 3.0 m/s^2 over a distance of  530 m.  What is its speed after traveling this distance?

29.  Decelerating a plane at the uniform rate of 8.0 m/s^2 (a = -8.0 m/s^2), a pilot stops the plane in  +484m.  How fast was the plane going before braking began?

30.  A box falls off the tailgate of a truck and slides along the street for a distance of 62.5 m. Friction decelerates the box at 5.0 m/s^2.  At what speed was the truck going when the box fell?

ACCELERATION DUE TO GRAVITY:  The equations to solve "falling body" problems are similar to the equations that you have used for horizontal motion. The difference is that the acceleration variable a becomes a gravitational acceleration value g. For the planet earth, near its surface, the value for g is defined as 9.81 kg m / s2
The common equations used for falling bodies are as follows.

 vf = vi + gt              vf^2 = vi^2 + 2gd           d = vit + 0.5 g t^2
 

Practice problem A:  How far will an object fall in earth's gravity during a 5 second interval?

Practice problem B:  If an object at rest is allowed to free fall a distance of 250 m, how fast will it be going at 250 m below where it started from?

Practice problem C:  What is the value for g on a planet which causes an object to free fall from 15 m/s to 115 m/s in 10 s?

The following are Links to Homework Graphing Assignments:

WB PS#3-2, numbers 1-3

WB PS#3-2, numbers 4-5

WB PS#4-3, numbers 1-3

WB PS#4-4, numbers 5-6