Let's analyze each distance-time graph and match it with the correct description based on what the slope of the graph represents.
In a
distance-time graph:
- The
slope of the line represents the
speed of the object.
- A
straight line with constant slope → constant speed.
- A
horizontal line (zero slope) → object is stopped (no change in distance).
- A
curved line with decreasing slope → speed is decreasing.
- A
line going downward → distance is decreasing, meaning the object is moving back toward the starting point.
---
Graph A:
- This is a
straight diagonal line starting from the origin and increasing at a constant rate.
- The slope is
constant and positive, meaning the car is moving away from the starting point at a
constant speed.
✔ Matches Description 2: *The car is traveling at a constant speed.*
> Because the distance increases uniformly over time, indicating constant speed.
---
Graph B:
- This is a
straight diagonal line going
downward from left to right.
- The slope is
constant and negative, meaning the distance from the starting point is decreasing at a constant rate.
✔ Matches Description 4: *The car is coming back.*
> Because the distance from the starting point is decreasing over time, which means the car is moving back toward the origin.
---
Graph C:
- This is a
horizontal line, meaning the distance does not change over time.
- The slope is zero → no motion.
✔ Matches Description 1: *The car is stopped.*
> Because the distance remains constant, indicating the car is not moving.
---
Graph D:
- This is a
curve that starts steep and gradually flattens out.
- The slope is
positive but decreasing, meaning the car is moving forward but slowing down.
✔ Matches Description 3: *The speed of the car is decreasing.*
> Because the slope of the curve (which represents speed) decreases over time, showing that the car is slowing down as it moves forward.
---
Final Answers:
Graph A matches description 2 because the distance increases at a constant rate, indicating constant speed.
Graph B matches description 4 because the distance decreases over time, meaning the car is returning toward the starting point.
Graph C matches description 1 because the distance remains constant over time, meaning the car is stationary.
Graph D matches description 3 because the slope of the graph decreases over time, indicating that the car’s speed is decreasing.
Parent Tip: Review the logic above to help your child master the concept of interpreting motion graphs worksheet.
