LINEAR MOTION

Chapter 4

PuzzlerQUESTION:

Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you, and the other is 3 meters upstream from you. Which can you swim to in the shortest time?

a.The preserver upstream b.The preserver downstream c.Each swim requires the same time.

downstream

Puzzler Answer

ANSWER: CTo get a grip on this, pretend that you are in a swimming pool on a fast-moving ocean liner. If both life preservers are the same distance from

you in the pool, swimming toward either would take the same time. The speed of the liner through the

water makes no difference, just as it makes no difference to people playing shuffleboard or

billiards. Can you see that, in the flowing river, you're like a person in a pool aboard a moving

ocean liner—that swimming toward either preserver takes the same time?

All objects have uniform motion; they are all in (dynamic) equilibrium.

One-Dimensional Motion and Distance

Motion in one dimension refers to straight-line motion (Linear)Example: train traveling on a straight track

Motion and Frame of Reference

Motion– a change in position

Frame of reference– A point against which position is measured

Example: A train traveling between stations– It is in motion when measured against the track.– It is stationary when measured against a seat.

DETECTING MOTION

In order to see an object in motion, you need to compare it to a frame of reference, such as a stationary background.

RELATIVE MOTION WEB SITES

http://www.phy.ntnu.edu.tw/java/relativeVelocity/relativeVelocity.htmlDetermine the displacement and distance for the journey illustrated below.

120 m north, 57 m south, 5 minute rest, 78 m south, 40 m north, 67 m north, 99 m south, 7 minute rest, 42 m north.

Displacement (x) vs. Distance (d)

Displacement means straight line distance from the initial position to the final position (change in position)Distance means the total length of the path traveled by an object.

•Keep in mind that distance is the addition of all lengths of the path traveled by an object in all directions.

5 m

7 m

5 m = 17 m

Think:

How is it possible for a car to travel a distance of 5 miles, and have a displacement is equal to zero.Drive around a very long block and return to the starting position. Back out of your garage, drive 5 miles, and return to your garage.

Average Velocity• Average velocity is total displacement divided by the

time interval during which the displacement occurred.

Average speed equation is written v = d/tv is average speed t is time d is distance

Section 1 Displacement and VelocityChapter 2

Average Velocity

The units can be determined from the equation.– SI Units: meters per second or m/s– Other Possible Units: mi/h, km/h, cm/year

Classroom Practice Problems

A car travels 36 km to the north in 30.0 min. Find the average velocity in km/min and in km/h.– Answer: 1.2 km/min to the north or 72 km/h to the north

A car travels 100.0 km to the east. If the first half of the distance is driven at 50.0 km/h and the second half at a 100.0 km/h, what is the average velocity?– Answer: 66.7 km/h to the east

Constant Velocity

• Object maintains the same speed in the same direction

• Example: Car travels at 35 km/h due east

Speed

Speed does not include direction while velocity does.Speed uses distance rather than displacement.In a round trip, the average velocity is zero but the average speed is not zero.

Velocity and Speed

Velocity describes motion with both a direction and a numerical value (a magnitude).

Speed has no direction, only magnitude.

Graphing MotionPosition (distance) vs. Time Graphs

At rest, no change in position

Graphing MotionPosition (distance) vs. Time Graphs

Yellow line (constant speed of 3 m/s) Blue line (constant speed of 1 m/s)

The velocity of the object can be calculated by evaluating the slope of each line, or one point along each line.

The objects shown by the yellow and blue lines are covering equal amounts of distance in equal amounts of time.

Graphing MotionPosition (distance) vs. Time Graphs

Changing distance over time or acceleration.

The object represented by the yellow line is covering a greater amount of distance with each unit of time that passes. (it is speeding up)

Graphing Motion (position vs. time)What type of motion does this graph show?

– Answer: Constant speed (straight line)

What is the slope of this line?– Answer: 1 m/s

What is the average velocity?– Answer: 1 m/s

Graphing MotionDescribe the motion of each object.Answers– Object 1: constant velocity to the

right or upward– Object 2: constant velocity of

zero (at rest)– Object 3: constant velocity to the

left or downward

PuzzlerQUESTION:

Suppose you and a pair of life preservers are floating down a swift river, as shown. You wish to get to either of the life preservers for safety. One is 3 meters downstream from you, and the other is 3 meters upstream from you. Which can you swim to in the shortest time?

a.The preserver upstream b.The preserver downstream c.Each swim requires the same time.

Would this situation change if the life preservers were fixed in place relative to the swimmer and the river’s current?

HOW CAN YOU TELL THAT AN OBJECT IS MOVING?

THE MOTION OF ONE OBJECT MAKES SENSE ONLY WHEN IT IS COMPARED TO ANOTHER OBJECT THAT HAS A DIFFERENT MOTION.

SENSING MOTION

We cannot sense uniform motion (mechanical equilibrium) unless we can compare our motion to an object with different motion. We can only sense changes in uniform motion, which is acceleration.

THE FATHERS OF MOTION: Falling Objects

Aristotle (~300 BC) hypothesized that heavier objects fell faster than lighter objects.Galileo (~1500’s) tested Aristotle’s hypothesis about falling objects and proved it wrong.Sir Isaac Newton (late 1600’s) extended Galileo’s work into three laws of motion and the universal law of gravitation.Newton showed that the universe ran according to natural laws.