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Understanding Motion Problems: Calculating Distance, Time, and Speed

This guide explores essential concepts of motion problems in physics, focusing on the relationships between speed, distance, and time. Through detailed examples, including scenarios involving driving speeds, distances to destinations, and timing of travel, we address common problems such as how long it takes to meet someone halfway, determine distances based on travel rates, and comprehend the situation when moving in opposite directions. Ideal for students and anyone seeking to grasp motion equations effectively.

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Understanding Motion Problems: Calculating Distance, Time, and Speed

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  1. How FAST should I travel to reach her?! MOTION PROBLEMS What TIME will he arrive?  How FAR is his office from my house?

  2. RATE • the ratio between distance and time D ______ = R T

  3. RATE D D _____ R = T R T

  4. DISTANCE D D = R x T R T

  5. TIME D D _____ T = R R T

  6. PROBLEM NO. 1 Dr. Reyes drove from his home to a medical mission at the rate of 65 kph. In going home, tired from work, he drove at the rate of 50 kph. If it took him one hour more in going home than in going to the mission, how far is the mission site from his home? (Assume that he passed through the same road).

  7. Table for Representation Rate (kph) Time (hrs) Distance (km) From his home to the medical mission x 65 65x From the medical mission to his home 50 x + 1 50 (x + 1) FORMULA? BACK to the PROBLEM

  8. FOR THE WORKING EQUATION: 65 x EQUALS 50 (x + 1)

  9. SOLUTION: 65x = 50 (x + 1) 65x = 50x + 50 15x 50 = 50 15 x = 10 3 x = hours BACK to the REPRESENTATION

  10. DISTANCE = ? D = 65x = 65 The mission site is 650 3 = km from the house. km =

  11. PROBLEM NO. 2 Clarissa’s office is 28 km from her house. Upon reaching the office, she realized she forgot her cell phone. Since she is expecting a very important call from her client, Paolo, she decided to go back home and get it. At home, however, her grandma noticed the phone and asked Clarissa’s mom to go to Clarissa’s office to give it. If they live their respective places at the same time, and Clarissa is traveling 80 kph and her mom at 60 kph, after how many hours will they meet on the road? (Assume they will use the same road.)

  12. Table for Representation Rate (kph) Time (hrs) Distance (km) Clarissa 80 x 80 x 60 60 x Mom x BACK to the PROBLEM

  13. FOR THE WORKING EQUATION: 60 x + = 80 x 28 km 28 km 60 x 80 x

  14. SOLUTION: 80 x + 60 x = 28 140 x = 28 28 140 x = Clarissa and her mom will meet after 12 minutes. 1 5 = hour Or x 12 minutes BACK to the REPRESENTATION

  15. PROBLEM NO. 3 Jaime and Pearl left their home and traveled in opposite directions. Jaime went to his client and drove at the rate of 72 kph and Pearl drove at 54 kph to school. When will they be 168 km apart? 168 km

  16. Table for Representation Rate (kph) Time (hrs) Distance (km) 72 x 72 x Jaime 54 x 54 x Pearl BACK to the PROBLEM

  17. FOR THE WORKING EQUATION: 72 x 54 x 168 km + 54 x = 72 x 168 BACK to the PROBLEM

  18. SOLUTION: + 54 x = 72 x 168 126 x Jaime and Pearl will be 168 km apart after = 168 168 126 x = 4 3 x = hours (1 hour and 20 minutes). or hours BACK to the REPRESENTATION

  19. PROBLEM NO. 4 Ms. Buenavides was in a hurry when she left her office to attend a meeting. She instructed her driver to drive at the rate of 60 kph. Her assistant head, Mr. Dabuet, followed after 1 hour traveling at the rate of 84 kph. When will Mr. Dabuet overtake Ms. Buenavides if they started at the same place and used the same path?

  20. A F T E R 1 H O U R:

  21. Table for Representation Rate (kph) Time (hrs) Distance (km) Ms. Buenavides 60 x + 1 60 (x + 1) Mr. Dabuet 84 x 84 x BACK to the PROBLEM

  22. FOR THE WORKING EQUATION: 60 (x + 1) E Q U A L S 84 x 60 (x + 1) = 84 x

  23. SOLUTION: 60 (x + 1) = 84 x 60 x + 60 = 84 x 60 = 24 x 60 24 x = 5 2 x = or hours BACK to the REPRESENTATION

  24. After traveling for hrs, Dr. Dabuet will overtake Dr. Buenavides.

  25. T H A N K Y O U F O R L IS T E N ING! ! !

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