Displacement and Distance

Distance and Displacement

by Jamaica Ortega

Lesson 31.2

​Learning Objective:

​Determine the total distance and total displacement an object covers within the duration of its motion.

Multiple Select

In describing the motion of an object, you shall make use of the five descriptors of motion. Identify the five descriptors of motion.

• distance and displacement

• force and mass

• speed and velocity

• tension

• acceleration

• ​Motion may be described by specifying how far something has traveled in changing position and time.

• ​The total path traversed by an object moving from one location to another is known as distance,

• ​while the separation of that object and a reference point is known as displacement

• ​Distance is a scalar quantity which has only magnitude

• ​Displacement is a vector quantity which has both magnitude and direction

Conceptual Example 1

• Based on the picture, the distance between the boy and the Physics Laboratory as well as the distance between the girl and the Physics Laboratory is 5.0 m

• ​The displacement of the boy as he moves in a straight line from his original is 5.0 m East.

• ​The displacement of the girl as he moves in a straight line from his original is 5.0 m West.

Conceptual Example 1

• Even though both students move along equal distances, their displacements are different because of the difference in their directions - the boy moves to the east while the girl moves to the west.

Conceptual Example 2

• ​​Refer to Figure 2. A man walks along a straight- line path.

• ​He walks from point A then to point B and back to point C.

• ​What is the man’s total distance?

• ​From point A to B, he covers

• 8 m. From point B to C, he covers 3 m.

• ​Therefore, his total distance is 11 m.

Conceptual Example 2

• ​​What about his displacement

• (​IMPORTANT: Take note of the initial and final positions.)

• ​The initial position is at Point A, while the final position is at Point C.

• ​The gap between Points A and C measures 5 m.

• ​Therefore from his initial position his displacement is 5 m East.

What if?

• ​The man’s initial motion covers a path from Point A to Point B and to Point C. What if he walks all the way back to Point A? What will his distance and displacement be?

• ​Previously, from Points A-B-C, his total distance is 11 m. Now covering Point C to A, which is 5 m in gap, his total distance is now 16 m.

• ​For his displacement, his initial and final positions are both at Point A, making his displacement zero.

How can displacement be zero?

• ​Take note that previously, his initial position is at Point A and is displaced at Point C which is his final position. This, therefore, presents a gap between initial and final positions and this gap is the displacement.

• ​But now, his initial and final positions are THE SAME, which means the man is not displaced at all. Therefore, no gap is made between initial and final

​Before our Quick Check, take note of the Stoplight Reminders.

Fill in the Blanks

Multiple Choice

What is his total DISPLACEMENT, covering Points A,

B, C, and D, respectively?

• 6 m, East

• 24 m, East

• 27 m, East

• 63 m, East

Multiple Choice

If his total path covers Points A, B, C, D, and

back to A, what is his total distance? His

displacement?

• Distance = 90 m

  Displacement = 90 m, West

• Distance = 90 m

  Displacement = 0 m

• Distance = 54 m

  Displacement = 0 m

• Distance = 54 m

  Displacement = 54 m, West

Fill in the Blanks

Multiple Choice

What will be his total DISPLACEMENT be if he

covers Points C, A, B and D respectively, with Point C as the initial position?

• 27 m, East

• 21 m, East

• 24 m, East

• 18 m, East

Conceptual Example 3

• ​​Refer to Figure 3. Two people are rowing a boat towards different directions, going 500 meters South, then 600 meters East, and then 500 meters North.

• ​What is the total distance covered?

• ​By simply adding 500 m, 600 m, and 500 m,

• ​The total distance is 1600 m

Conceptual Example 3

• ​​Refer to Figure 3. Two people are rowing a boat towards different directions, going 500 meters South, then 600 meters East, and then 500 meters North.

• ​What is the displacement?

• ​With Point A as the initial position and Point D as the final position,

• ​The displacement is 600 m, East.

Fill in the Blanks

Fill in the Blanks

WHAT IF?

• ​What if the two people row the boat from Point A to Point B up until Point C? What is the total distance covered? What is the displacement?

• ​They cover 500 m from Point A to B and another 600 m to Point C. Adding them all together

• ​the total distance covered is 1100 meters

WHAT IF?

• ​However, seeing that the initial position is at Point A and the final position is at Point C, there is no label in the figure on how far they are at each other. So, HOW?

• ​Notice how the paths of A-B and B-C form a right triangle together with the path of A-C. You can use the Pythagorean Theorem to look for the displacement.

WHAT IF?

• ​Using the Pythagorean Theorem, to find the displacement from A to C.

• ​c² = a² + b²

• ​​c² = 500² + 600²

• ​​c² = 610,000

• ​(get the square root of both sides)

• ​c = 781.02

• ​The displacement is 781.02 m, Southeast

​

THINK ABOUT IT!

• In a straight-line motion:

• ​Can displacement be equal to distance?

• ​YES.

• ​Can displacement be less than distance?

• ​YES.

• ​Can displacement be greater than distance?

• ​NO

Multiple Choice

On his way to school, Iggy travelled 100 m North, 300 m East, 100 m South, 100 m West. What is his displacement. (Tip: Sketch the Problem)

• 300 m, East

• 100 m, South

• 200 m, East

​Conceptual Attainment

​Relative Motion, Distance and Displacement

Open Ended

Elaborate your answer for each situation (9 pts)

You are inside a vehicle, watching the busy city road outside your window. Suddenly, another vehicle drives right beside, and maintains the same speed as yours. You watch another person inside busy playing with his phone. As you observe him while his car maintains the same speed, how will you describe the motion of that person

(a) relative to the ground, (b) relative to you, (c) relative to his car?

Open Ended

Elaborate your answer for each situation (9 pts)

Can you drive your car in such a way that the distance it covers is true with the following statements? Give an example for each.

(a) Greater than the magnitude of the displacement

(b) Equal to the magnitude of the displacement

(c) Less than the magnitude of the displacement