Velocity-Time Graph Worksheet with questions and a data table for plotting car positions over time.

Let’s solve Part I, Question 1 step by step using the velocity-time graph provided.

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Understanding the Graph:

- Y-axis: Velocity in km/h (from 0 to 80.0)
- X-axis: Time in hours (from 0 to 1.1)
- The graph shows how the car’s speed changes over time.
- Acceleration = slope of the velocity-time graph (rise/run = Δv/Δt)
- Stopped = velocity = 0
- Greatest velocity = highest point on the graph
- Accelerating = positive slope (velocity increasing)
- Decelerating = negative slope (velocity decreasing)
- Constant velocity = horizontal line (slope = 0)

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## Question 1a: At what time was the car stopped?

Look for where the velocity = 0 km/h.

From the graph:
- From t = 0.7 h to t = 0.8 h, the velocity is 0 → the car is stopped.

✔ Answer: 0.7 h to 0.8 h

*(Note: Since it says “at what time”, and it’s stopped for a duration, you may write the interval or say “between 0.7 and 0.8 hours”.)*

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## Question 1b: At what time did the car have the greatest velocity?

Find the highest point on the graph.

- The graph reaches 60.0 km/h starting at t = 0.2 h and stays there until t = 0.4 h.

So, the car has its greatest velocity from 0.2 h to 0.4 h.

✔ Answer: Between 0.2 h and 0.4 h

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## Question 1c: What was the greatest velocity?

Read the y-value at the highest point.

- It’s clearly 60.0 km/h

✔ Answer: 60.0 km/h

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## Question 1d: At what time(s) was the car accelerating?

Acceleration occurs when velocity is increasing → positive slope.

Look for upward-sloping segments:

1. From t = 0 h to t = 0.2 h → velocity increases from 0 to 60 km/h → accelerating
2. From t = 0.8 h to t = 1.0 h → velocity increases from 0 to 40 km/h → accelerating

✔ Answer: From 0 to 0.2 h, and from 0.8 to 1.0 h

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## Question 1e: How fast was the car going at 1.0 h?

Find t = 1.0 h on x-axis → go up to the graph → read y-value.

At t = 1.0 h, velocity = 40.0 km/h

✔ Answer: 40.0 km/h

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## Question 1f: What is the acceleration at 0.9 h?

Acceleration = slope of velocity-time graph at that point.

At t = 0.9 h, the car is in the segment from 0.8 h to 1.0 h, where velocity increases from 0 to 40 km/h.

Calculate slope:

- Δv = 40.0 km/h - 0 km/h = 40.0 km/h
- Δt = 1.0 h - 0.8 h = 0.2 h

→ Acceleration = Δv / Δt = 40.0 / 0.2 = 200 km/h²

✔ Answer: 200 km/h²

*(Note: Units are km/h per hour, so km/h² — this is acceptable for graphical analysis unless SI units are required.)*

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## ✔ Final Answers for Part I, Question 1:

a. 0.7 h to 0.8 h
b. Between 0.2 h and 0.4 h
c. 60.0 km/h
d. From 0 to 0.2 h, and from 0.8 to 1.0 h
e. 40.0 km/h
f. 200 km/h²

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## 📌 Part 2: Position-Time Data for Two Cars

You’re asked to:

1. Graph the data for Car A and Car B on the same position-time graph.
2. Compute the velocity of each car.

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Step 1: Plot the Points

Given table:

| TIME (min) | CAR A (km) | CAR B (km) |
|------------|------------|------------|
| 0 | 0 | 2 |
| 2 | 2 | 3.5 |
| 4 | 4 | 5 |
| 6 | 6 | 6.5 |
| 8 | 8 | 8 |

Plot these points on the provided graph (position vs. time).

- Car A: Points: (0,0), (2,2), (4,4), (6,6), (8,8) → straight line through origin with slope 1
- Car B: Points: (0,2), (2,3.5), (4,5), (6,6.5), (8,8) → also a straight line, starting at (0,2)

Both cars have constant velocity (straight lines).

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Step 2: Compute Velocity

Velocity = change in position / change in time = Δx / Δt

#### For Car A:

Use any two points, e.g., from t=0 to t=8 min:

- Δx = 8 km - 0 km = 8 km
- Δt = 8 min - 0 min = 8 min

→ Velocity = 8 km / 8 min = 1 km/min

But usually we convert to km/h:

1 min = 1/60 hr → 1 km/min = 60 km/h

✔ Car A velocity: 60 km/h

*(Alternatively, since every 2 minutes, it moves 2 km → 1 km/min → 60 km/h)*

#### For Car B:

Use t=0 to t=8 min:

- Δx = 8 km - 2 km = 6 km
- Δt = 8 min

→ Velocity = 6 km / 8 min = 0.75 km/min

Convert to km/h: 0.75 × 60 = 45 km/h

✔ Car B velocity: 45 km/h

*(Check with another interval: from t=2 to t=4 min: Δx = 5 - 3.5 = 1.5 km, Δt = 2 min → 1.5/2 = 0.75 km/min → same result)*

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## ✔ Final Answers for Part 2:

- Graph: Plot both sets of points. Car A is a straight line from (0,0) to (8,8). Car B is a straight line from (0,2) to (8,8).
- Velocities:
- Car A: 60 km/h
- Car B: 45 km/h

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## 🎯 Summary:

You’ve now solved all parts using graphical analysis as requested.

Let me know if you’d like me to sketch the graphs for you or explain further!