Worksheet Velocity Graph 1.docx - Section: Name: Date: Velocity - Free Printable

Let's analyze the speed-time graph provided in the question step by step and answer all parts.

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(i) Using the graph, determine:

#### a) The MAXIMUM speed

- From the graph, we observe that the highest value on the speed axis reached is 12 m/s.
- This occurs at t = 6 s to t = 10 s, where the speed remains constant at 12 m/s.

✔ Answer:
Maximum speed = 12 m/s

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#### b) The number of seconds for which the speed was constant

- The speed is constant when the graph is a horizontal line (flat).
- From the graph:
- Between t = 6 s and t = 10 s, the speed stays at 12 m/s.
- Duration = $10 - 6 = 4$ seconds

✔ Answer:
4 seconds

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#### c) The TOTAL distance covered by the athlete during the race

> 🔹 Important Concept:
In a speed-time graph, the area under the graph represents the distance traveled.

We can break the graph into three parts:

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1. From t = 0 to t = 6 s:
- This is a right triangle with:
- Base = 6 s
- Height = 12 m/s
- Area = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 12 = 36$ meters

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2. From t = 6 to t = 10 s:
- This is a rectangle:
- Width = $10 - 6 = 4$ s
- Height = 12 m/s
- Area = $4 \times 12 = 48$ meters

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3. From t = 10 to t = 13 s:
- This is another triangle (deceleration):
- Base = $13 - 10 = 3$ s
- Height = 12 m/s
- Area = $\frac{1}{2} \times 3 \times 12 = 18$ meters

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Total Distance = $36 + 48 + 18 = 102$ meters

✔ Answer:
Total distance = 102 meters

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(ii) During which time-period of the race was:

#### a) The speed of the athlete increasing

- Speed increases when the graph is rising upward.
- This happens from t = 0 s to t = 6 s

✔ Answer:
0 to 6 seconds

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#### b) The speed of the athlete decreasing

- Speed decreases when the graph is falling downward.
- This happens from t = 10 s to t = 13 s

✔ Answer:
10 to 13 seconds

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#### c) The acceleration of the athlete zero?

> 🔹 Acceleration = slope of the speed-time graph
- If the slope is zero → the graph is horizontal → speed is constant → acceleration = 0

From the graph, this occurs between t = 6 s and t = 10 s

✔ Answer:
6 to 10 seconds

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✔ Final Answers Summary:

#### (i)
a) Maximum speed = 12 m/s
b) Time with constant speed = 4 seconds
c) Total distance = 102 meters

#### (ii)
a) Speed increasing = 0 to 6 seconds
b) Speed decreasing = 10 to 13 seconds
c) Acceleration zero = 6 to 10 seconds

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This completes the solution. Let me know if you'd like a diagram sketch or further explanation!