Question

the distance - time graphs below represent the motion of a car. match the descriptions with the graphs. explain your answers.
descriptions:

1. the car is stopped.
2. the car is traveling at a constant speed.
3. the speed of the car is decreasing.
4. the car is coming back.

Explanation:

1. For "The car is stopped": In a distance - time graph, when the distance remains constant as time passes, the car is not moving. Graph C has a horizontal line, meaning distance doesn't change with time, so it matches this description.
2. For "The car is traveling at a constant speed": A distance - time graph with a straight - line (constant slope) represents constant speed because speed $v=\frac{\Delta d}{\Delta t}$, and a constant slope means a constant ratio of distance change to time change. Graph A is a straight line through the origin, so it has a constant slope, matching this description.
3. For "The speed of the car is decreasing": The slope of a distance - time graph represents speed. If the slope is getting smaller (the graph is curving and the rate of increase of distance with time is decreasing), the speed is decreasing. Graph D is a curve that is flattening out, so its slope is decreasing, matching this description.
4. For "The car is coming back": When the distance from the starting point is decreasing as time increases, the car is moving back towards the start. Graph B shows distance decreasing with time (a negative slope), so it matches this description.

Answer:

1. The car is stopped: C
2. The car is traveling at a constant speed: A
3. The speed of the car is decreasing: D
4. The car is coming back: B