Distance-Time Graphs Worksheet Answers - Free Printable

Problem Analysis:

The given graph is a distance-time graph that shows the movement of a car from point A to point D. The graph has two slant lines (AB and CD) indicating motion, and one flat line (BC) indicating that the car is stationary. We need to solve several questions based on this graph.

Key Observations from the Graph:

1. Point A: The car starts at 0 meters at time 0 seconds.
2. Segment AB: The car moves from 0 meters to 200 meters in 10 seconds.
3. Segment BC: The car is stationary from 10 seconds to 30 seconds (flat line).
4. Segment CD: The car moves from 200 meters to 500 meters in 30 seconds (from 30 seconds to 60 seconds).

Solution to Each Question:

#### 1. What is the speed of the car on its journey from C to D?
- Distance traveled from C to D:
- Distance at point C = 200 meters
- Distance at point D = 500 meters
- Change in distance = \( 500 - 200 = 300 \) meters

- Time taken from C to D:
- Time at point C = 30 seconds
- Time at point D = 60 seconds
- Change in time = \( 60 - 30 = 30 \) seconds

- Speed:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{300 \text{ meters}}{30 \text{ seconds}} = 10 \text{ m/s}
\]

Answer:
\[
\boxed{10 \text{ m/s}}
\]

---

#### 2. On which part of the journey did the car travel faster?
- Speed from A to B:
- Distance = \( 200 - 0 = 200 \) meters
- Time = \( 10 - 0 = 10 \) seconds
- Speed = \( \frac{200}{10} = 20 \text{ m/s} \)

- Speed from C to D:
- Distance = \( 500 - 200 = 300 \) meters
- Time = \( 60 - 30 = 30 \) seconds
- Speed = \( \frac{300}{30} = 10 \text{ m/s} \)

Comparing the speeds:
- Speed from A to B = 20 m/s
- Speed from C to D = 10 m/s

The car traveled faster from A to B.

Answer:
\[
\boxed{\text{A to B}}
\]

---

#### 3. Calculate the speed of the car during the first 10 seconds!
- Distance traveled in the first 10 seconds:
- From point A to point B, the car travels from 0 meters to 200 meters.
- Distance = \( 200 - 0 = 200 \) meters

- Time taken:
- Time = 10 seconds

- Speed:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{200 \text{ meters}}{10 \text{ seconds}} = 20 \text{ m/s}
\]

Answer:
\[
\boxed{20 \text{ m/s}}
\]

---

#### 4. For how long did the car stop?
- The car stops during the segment BC.
- Time at point B: 10 seconds
- Time at point C: 30 seconds
- Duration of stop:
\[
\text{Duration} = 30 - 10 = 20 \text{ seconds}
\]

Answer:
\[
\boxed{20 \text{ seconds}}
\]

---

#### 5. What is the average speed of the car for the whole journey?
- Total distance traveled:
- Final distance at point D = 500 meters
- Initial distance at point A = 0 meters
- Total distance = \( 500 - 0 = 500 \) meters

- Total time taken:
- Final time at point D = 60 seconds
- Initial time at point A = 0 seconds
- Total time = \( 60 - 0 = 60 \) seconds

- Average speed:
\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{500 \text{ meters}}{60 \text{ seconds}} = \frac{50}{6} \approx 8.33 \text{ m/s}
\]

Answer:
\[
\boxed{8.33 \text{ m/s}}
\]

---

#### 6. What is the average speed of the car for the time it was moving?
- Total distance traveled (same as before): 500 meters
- Total time spent moving:
- Time from A to B: 10 seconds
- Time from C to D: 30 seconds
- Total moving time = \( 10 + 30 = 40 \) seconds

- Average speed while moving:
\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total moving time}} = \frac{500 \text{ meters}}{40 \text{ seconds}} = 12.5 \text{ m/s}
\]

Answer:
\[
\boxed{12.5 \text{ m/s}}
\]

---

Final Answers:

1. \(\boxed{10 \text{ m/s}}\)
2. \(\boxed{\text{A to B}}\)
3. \(\boxed{20 \text{ m/s}}\)
4. \(\boxed{20 \text{ seconds}}\)
5. \(\boxed{8.33 \text{ m/s}}\)
6. \(\boxed{12.5 \text{ m/s}}\)