Question

part 3 matching: in the space to the right, match each distance vs. time graph in 16 - 19 with the velocity vs time graph in a - d that shows the same type of motion. then next to each match, describe the motion that each graph pair shows. (ex. graph #2 matches graph z because both show an object that isnt moving.) 16. 17. 18. 19. (graphs: left side has distance - time graphs labeled 16,17,18,19; right side has velocity - time graphs labeled a,b,c,d)

Explanation:

Step1: Analyze Graph 16 (Distance - Time)

Graph 16 has a horizontal line for distance vs. time, meaning distance is constant over time. So velocity (rate of change of distance) is 0. We look for a velocity - time graph with velocity 0, which is Graph D (assuming D is a horizontal line at 0 velocity, though not fully shown, but from context, a constant 0 velocity graph). So 16 matches D. Motion: Object is at rest (distance doesn't change, velocity is 0).

Step2: Analyze Graph 17 (Distance - Time)

Graph 17 is a curved distance - time graph that is concave up (increasing slope). The slope of distance - time is velocity, so increasing slope means increasing velocity. So we need a velocity - time graph with increasing velocity, which is Graph A (a line with positive slope, increasing velocity). So 17 matches A. Motion: Object is accelerating (velocity is increasing as distance - time slope increases).

Step3: Analyze Graph 18 (Distance - Time)

Graph 18 is a straight line with positive slope in distance - time, meaning constant velocity (since slope is constant). So we need a velocity - time graph with constant velocity, which is Graph C (a horizontal line, constant velocity). So 18 matches C. Motion: Object is moving with constant velocity (distance increases linearly with time, velocity is constant).

Step4: Analyze Graph 19 (Distance - Time)

Graph 19 is a curved distance - time graph that is concave down (decreasing slope). The slope of distance - time is velocity, so decreasing slope means decreasing velocity. So we need a velocity - time graph with decreasing velocity, which is Graph B (a line with negative slope, decreasing velocity). So 19 matches B. Motion: Object is decelerating (velocity is decreasing as distance - time slope decreases).

Answer:

1. Matches D. Motion: Object is at rest (distance remains constant over time, so velocity is 0).
2. Matches A. Motion: Object is accelerating (distance - time graph has increasing slope, so velocity is increasing over time).
3. Matches C. Motion: Object is moving with constant velocity (distance - time graph has constant slope, so velocity is constant over time).
4. Matches B. Motion: Object is decelerating (distance - time graph has decreasing slope, so velocity is decreasing over time).

(Note: The exact labels of velocity - time graphs (A - D) assume standard interpretations: A - increasing velocity, B - decreasing velocity, C - constant velocity, D - zero velocity. Adjusted based on typical motion graph relationships.)