Question

connection: http://www.physicsclassroom.com/class/1dkin/u1l3b.html kinematic graphing: sublevels 1-4 (and some of sublevels 9-11) on can be described using words, diagrams, numerical information, equations, and graphs. descr on with graphs involves representing how a quantity such as the objects position can change with me. the key to using position-time graphs is knowing that the slope of a position-time graph rev mation about the objects velocity. by detecting the slope, one can infer about an objects velocity. e goes, so goes the velocity. view: categorize the following motions as being either examples of + or - acceleration. a. moving in the + direction and speeding up (getting faster) b. moving in the + direction and slowing down (getting slower) c. moving in the - direction and speeding up (getting faster) d. moving in the - direction and slowing down (getting slower) erpreting position-graphs on the graphs below, draw two lines/curves to represent the given verbal descriptions; label the lines/curves as a or b. tables with position-time graphs: a remaining at rest, b moving; a moving slow, b moving fast; a moving in + direction, b moving in - direction; a moving at constant speed, b accelerating; a move in + dirn; speed up, b move in + dirn; slow dn; a move in - dirn; speed up, b move in - dirn; slow dn for each type of accelerated motion, construct the appropriate shape of a position-time graph. moving with a + velocity and a + acceleration moving with a + velocity and a - acceleratio

Explanation:

Part 1: Categorizing Acceleration (a - d)

To determine the sign of acceleration, we use the rule: Acceleration has the same sign as velocity when speeding up, and the opposite sign when slowing down. Velocity sign is based on direction (+ or -).

a. Moving in + direction, speeding up

• Velocity (\(v\)): \(+\) (direction)
• Speeding up: Acceleration (\(a\)) same sign as \(v\) → \(a = +\)

b. Moving in + direction, slowing down

• Velocity (\(v\)): \(+\)
• Slowing down: Acceleration (\(a\)) opposite sign to \(v\) → \(a = -\)

c. Moving in - direction, speeding up

• Velocity (\(v\)): \(-\)
• Speeding up: Acceleration (\(a\)) same sign as \(v\) → \(a = -\)

d. Moving in - direction, slowing down

• Velocity (\(v\)): \(-\)
• Slowing down: Acceleration (\(a\)) opposite sign to \(v\) → \(a = +\)

Part 2: Interpreting Position - Time Graphs

Graph 1: Remaining at rest (A) vs. Moving (B)

• A (Rest): Horizontal line (position constant over time).
• B (Moving): Sloped line (position changes with time).

Graph 2: Moving slow (A) vs. Moving fast (B)

• Slope of position - time graph = velocity. Steeper slope = faster speed.
• A (Slow): Less steep slope.
• B (Fast): Steeper slope.

Graph 3: Moving in + direction (A) vs. Moving in - direction (B)

• A (+ direction): Positive slope (position increases with time).
• B (- direction): Negative slope (position decreases with time).

Graph 4: Moving at constant speed (A) vs. Accelerating (B)

• A (Constant speed): Straight line (constant slope = constant velocity).
• B (Accelerating): Curved line (slope changes, so velocity changes).

Graph 5: Move in + dirn; speed up (A) vs. Move in + dirn; slow dn (B)

• A (Speed up in + dir): Curved line with increasing slope (velocity increasing, since speed up in + direction).
• B (Slow down in + dir): Curved line with decreasing slope (velocity decreasing, since slow down in + direction).

Graph 6: Move in - dirn; speed up (A) vs. Move in - dirn; slow dn (B)

• A (Speed up in - dir): Curved line with increasing magnitude of negative slope (velocity becoming more negative, speed up in - direction).
• B (Slow down in - dir): Curved line with decreasing magnitude of negative slope (velocity becoming less negative, slow down in - direction).

Part 3: Position - Time Graphs for Accelerated Motion

Moving with + velocity and + acceleration

• Velocity is positive (slope positive), acceleration is positive (slope increasing). So the graph is a curve opening upwards (concave up) with a positive, increasing slope.

Moving with + velocity and - acceleration

• Velocity is positive (slope positive), acceleration is negative (slope decreasing). So the graph is a curve opening downwards (concave down) with a positive, decreasing slope.

Answer:

s (Acceleration Categorization)
a. \(\boldsymbol{+}\)
b. \(\boldsymbol{-}\)
c. \(\boldsymbol{-}\)
d. \(\boldsymbol{+}\)

(For graph drawing, follow the explanations above to sketch the lines/curves.)