2.1 Displacement

• Cyclists in Vietnam are described by their position relative to buildings and a canal.
• The frame of reference can be used to describe their motion.
• Where it is at a certain time.

• You need to specify its position relative to the reference frame.
• Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame.
• A professor's position could be described in terms of where she is in relation to the white board, while a rocket launch would be described in terms of the position of the rocket with respect to the Earth as a whole.
• In some cases, we use reference frames that are moving relative to the Earth.
• The reference frame for the position of a person in an airplane is the airplane, not the Earth.
• If an object moves relative to a reference frame, the object's position changes.
• Displacement is when an object has moved or been displaced.

• The upper case Greek letter Delta always means "Change in" whatever quantity follows it.
• If you want to solve for displacement, subtract initial position from final position.

• The SI unit for displacement is the meter, but sometimes kilometers, miles, feet, and other units of length are used.
• When units other than the meter are used in a problem, you may need to convert them into meters to complete the calculation.

• A professor is lecturing.
• Her position is relative to Earth.
• The professor's displacement is represented by an arrow pointing to the right.

• A passenger is moving from his seat to the back of the plane.
• His location is relative to the airplane.
• The displacement of the passenger relative to the plane is represented by an arrow.
• The arrow representing his displacement is twice as long as the arrow representing the professor's displacement.

• There is a direction as well as a magnitude for displacement.
• The professor's displacement is 2.0 m to the right, while the airline passenger's displacement is 4.0 m to the rear.
• Direction can be specified with a plus or minus sign.
• When you start a problem, you can choose which direction you want to go, but you have to be positive.

• The motion to the right is positive while the motion to the left is negative.

• His displacement is negative because he is moving in the opposite direction of the plane.

• The distance is not described in terms of direction.
• The distance between two positions is not the same as the distance between them.
• There is no direction and no sign.
• The professor is walking at a distance of 2.0 m.

• There is a misconception about distance traveled vs.
• It is important to note that the distance traveled can be greater than the magnitude of the displacement, just a number with a unit.
• The professor could pace back and forth many times, perhaps walking a distance of 150 m during a lecture, yet still end up only 2.0 m to the right of her starting point.
• The magnitude of her displacement would be 2.0 m, but the distance she traveled would be 150 m. One way to think about this is to assume that you marked the beginning and end of the motion.
• The difference in the position of the two marks is what determines the displacement.
• The total length of the path between the two marks is the distance traveled.

• A cyclist rides 3 km west and 2 km east.

• The Eclipse Concept jet can be described in terms of the distance it traveled or its displacement in a specific direction.
• It is necessary to describe its displacement based on a coordinate system.
• In this case, it may be convenient to choose motion toward the left as positive motion, since the -coordinate runs from left to right, with motion to the right as positive and motion to the left as negative.

• displacement is defined by both direction and magnitude, distance is defined by magnitude Displacement is an example of a number.
• The distance is an example of a quantity.
• A force of 500 newtons straight down is an example of a vectors.

• The direction of a one-dimensional motion is given by a plus or minus sign.
• The arrows represent the Vectors graphically.
• An arrow points in the same direction as the vector if it is larger than the magnitude.

• There are some physical quantities that have no direction or are not specified.
• A person's height, a 90 km/h speed limit, a candy bar's calories, and a temperature are all variables with no direction.
• A temperature can be a negative scalar.
• The minus sign indicates a point on a scale.
• arrows are never used to represent scurrs.

• You must designate a coordinate system within the reference frame to describe the direction of a vector quantity.
• The coordinate system consists of a one-dimensional coordinate line.
• Motion to the right is considered positive while motion to the left is considered negative.

• Motion up is usually positive and motion down is negative with vertical motion.
• If you are analyzing the motion of falling objects, it can be useful to define them as the positive direction.
• It is useful to define left as the positive direction if people are running to the left in a race.
• It doesn't matter if the system is clear and consistent.
• You can't change a problem once you assign a positive direction.

• It's convenient to consider motion upward or to the right as positive, downward or to the left as negative.

• A person's speed can change as he or she rounds a corner.

• There is a quantity of speed.
• It has magnitude because it doesn't change at all with direction changes.
• Even if its magnitude remained constant, it would change as direction changes.

• The motion of racing snails can be described by their speeds.

• There is more to motion than that.
• We add definitions of time, velocity, and speed in this section.

• The most fundamental physical quantities are determined by how they are measured.

• This is the case with time.
• Measurement of time involves measuring a change in quantity.
• It could be a number on a digital clock, a heartbeat, or the position of the Sun in the sky.
• It is not possible to know if time has passed.

• The amount of time is compared to a standard.
• The SI unit for time is the second, abbreviated s. This allows us to determine a sequence of events by measuring the amount of time.

• We like to know how long it takes an airplane passenger to get from his seat to the back of the plane.
• To find elapsed time, we subtract the time at the beginning and end of the motion.
• The elapsed time would be 50 minutes if the lecture started at 11:00 A.M. and ended at 11:50 A.M.

• If the beginning time is zero, life is simpler.
• If we used a stopwatch, it would read zero at the start of the lecture and 50 min at the end.

• The scientific definition of velocity is the same as yours.
• If you have a large displacement in a small amount of time, you have a large velocity, and it has units of distance divided by time, such as miles per hour or kilometers per hour.

• The definition indicates that displacement is a vector.
• It has both direction and magnitude.
• The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h, and cm/s, are in common use.
• The negative sign indicates that the passenger is moving toward the back of the plane.

• The minus sign indicates the plane's average speed is in the back of the plane.

• The average speed of an object doesn't tell us anything about what happens between the beginning and end of the object.
• We can't tell from average speed whether the passenger stops or goes to the back of the plane.
• Smaller segments of the trip are needed to get more details.

• There is a more detailed record of the passenger going toward the back of the plane.

• The more detailed the information, the smaller the time intervals are.
• We are left with an infinitesimally small interval when we carry this process to its logical conclusion.
• The instantaneous velocity is the average velocity over an interval.
• The magnitude of the instantaneous velocity of the car is shown by the car's speedometer.

• Finding instantaneous velocity at a precise instant can involve taking a limit beyond the scope of this text.
• We can find precise values for instantaneous velocity.

• Most people use the terms "speed" and "velocity" interchangeably.
• They do not have the same meaning in physics.
• Speed has no direction.
• The speed is a number.

• We need to distinguish between instantaneous speed and average speed.

• The instantaneous velocity of the airplane passenger is 3.0 m/s, which is the minus meaning toward the rear of the plane.
• His instantaneous speed was 3.0 m/s.
• If you were to take a shopping trip at one time, your instantaneous speed would be 40 km/h.
• 40 km/h is the same as the magnitude but without a direction.
• Average speed is very different from average velocity.

• The magnitude of displacement can be less than the distance traveled.
• The average speed can be greater than the average velocity.
• If you drive to a store and return home in half an hour, your average speed was 12 km/h, because your car's odometer shows the total distance traveled was 6 km.
• Your displacement for the round trip is zero, so your average velocity was zero.
• Average speed isn't just the magnitude of average velocity.

• The total distance traveled is 6 km during a 30 minute trip to the store.
• The average speed is over 12 km/h.

• The average is zero.

• A graph is a way of showing the motion of an object.
• A plot of position can be useful.
• Given that we'll probably stop at the store, we're assuming that speed is constant.
• We will model it with no stops or changes in speed.

• The return trip is negative.