Question

match each word with its definition. match the items in the left column to the items in the right column.

1. the word that best describes 3, 0.5 s, 3m, 5 feet, and 78
2. the rate at which distance changes with respect to time--a scalar quantity
3. the word that best describes 5 mph north, 6 ft. left, 3 m/s east, and 10 meters south
4. the total distance divided by the total time traveled
5. the speed of an object at any instant
6. a change in displacement with respect to a change in time
7. the total displacement divided by the total time
8. the shortest distance between an initial and final position and the direction along that line; a vector quantity

right column: displacement, instantaneous speed, scalar, average speed, average velocity, speed, velocity, vector

Explanation:

To solve this matching problem, we analyze each term and its definition:

1. "the word that best describes 3, 0.5 s, 3m, 5 feet, and 78" → These are quantities with magnitude only (no direction), so they are scalar.
2. "the rate at which distance changes with respect to time--a scalar quantity" → This is the definition of speed (scalar, no direction).
3. "the word that best describes 5 mph north, 6 ft. left, 3 m/s east, and 10 meters south" → These have both magnitude and direction, so they are vector quantities.
4. "the total distance divided by the total time traveled" → This is the formula for average speed (scalar, based on distance).
5. "the speed of an object at any instant" → This is instantaneous speed (speed at a specific moment).
6. "a change in displacement with respect to a change in time" → Displacement is a vector, so this rate is velocity (vector quantity).
7. "the total displacement divided by the total time" → This is average velocity (vector, based on displacement).
8. "the shortest distance between an initial and final position and the direction along that line; a vector quantity" → This is the definition of displacement (vector, includes direction).

Final Matches:

1. scalar
2. speed
3. vector
4. average speed
5. instantaneous speed
6. velocity
7. average velocity
8. displacement

(To present as a list of matched pairs, e.g., 1 - scalar, 2 - speed, 3 - vector, 4 - average speed, 5 - instantaneous speed, 6 - velocity, 7 - average velocity, 8 - displacement)

Answer:

To solve this matching problem, we analyze each term and its definition:

1. "the word that best describes 3, 0.5 s, 3m, 5 feet, and 78" → These are quantities with magnitude only (no direction), so they are scalar.
2. "the rate at which distance changes with respect to time--a scalar quantity" → This is the definition of speed (scalar, no direction).
3. "the word that best describes 5 mph north, 6 ft. left, 3 m/s east, and 10 meters south" → These have both magnitude and direction, so they are vector quantities.
4. "the total distance divided by the total time traveled" → This is the formula for average speed (scalar, based on distance).
5. "the speed of an object at any instant" → This is instantaneous speed (speed at a specific moment).
6. "a change in displacement with respect to a change in time" → Displacement is a vector, so this rate is velocity (vector quantity).
7. "the total displacement divided by the total time" → This is average velocity (vector, based on displacement).
8. "the shortest distance between an initial and final position and the direction along that line; a vector quantity" → This is the definition of displacement (vector, includes direction).

Final Matches:

1. scalar
2. speed
3. vector
4. average speed
5. instantaneous speed
6. velocity
7. average velocity
8. displacement

(To present as a list of matched pairs, e.g., 1 - scalar, 2 - speed, 3 - vector, 4 - average speed, 5 - instantaneous speed, 6 - velocity, 7 - average velocity, 8 - displacement)