Problem Analysis:
The image provided is a speed-time graph, where the
y-axis represents speed in meters per second (m/s) and the
x-axis represents time in seconds (s). The graph shows different segments labeled as
A, B, C, D, each representing a distinct phase of motion. The task likely involves analyzing the motion described by this graph, such as calculating distances traveled, accelerations, or identifying specific characteristics of the motion.
Since the problem is not explicitly stated, I will infer a common task related to speed-time graphs:
calculating the total distance traveled by the object over the entire time interval (0 to 50 seconds). This can be done by finding the area under the speed-time graph.
---
Solution:
#### Step 1: Understand the Graph
The graph is divided into four segments:
1.
Segment A (0 to 10 seconds): The speed increases linearly from 0 m/s to 15 m/s.
2.
Segment B (10 to 20 seconds): The speed remains constant at 15 m/s.
3.
Segment C (20 to 30 seconds): The speed increases linearly from 15 m/s to 25 m/s.
4.
Segment D (30 to 50 seconds): The speed decreases linearly from 25 m/s to 0 m/s.
#### Step 2: Calculate the Area Under Each Segment
The area under a speed-time graph represents the distance traveled. We will calculate the area for each segment separately.
##### Segment A (0 to 10 seconds):
- Shape: Right triangle
- Base = 10 seconds
- Height = 15 m/s
- Area = \( \frac{1}{2} \times \text{base} \times \text{height} \)
\[
\text{Area}_A = \frac{1}{2} \times 10 \times 15 = 75 \, \text{meters}
\]
##### Segment B (10 to 20 seconds):
- Shape: Rectangle
- Base = 10 seconds
- Height = 15 m/s
- Area = \( \text{base} \times \text{height} \)
\[
\text{Area}_B = 10 \times 15 = 150 \, \text{meters}
\]
##### Segment C (20 to 30 seconds):
- Shape: Trapezoid
- Base 1 = 10 seconds
- Height 1 = 15 m/s
- Height 2 = 25 m/s
- Area = \( \frac{1}{2} \times (\text{height}_1 + \text{height}_2) \times \text{base} \)
\[
\text{Area}_C = \frac{1}{2} \times (15 + 25) \times 10 = \frac{1}{2} \times 40 \times 10 = 200 \, \text{meters}
\]
##### Segment D (30 to 50 seconds):
- Shape: Trapezoid
- Base = 20 seconds
- Height 1 = 25 m/s
- Height 2 = 0 m/s
- Area = \( \frac{1}{2} \times (\text{height}_1 + \text{height}_2) \times \text{base} \)
\[
\text{Area}_D = \frac{1}{2} \times (25 + 0) \times 20 = \frac{1}{2} \times 25 \times 20 = 250 \, \text{meters}
\]
#### Step 3: Sum the Areas
The total distance traveled is the sum of the areas under all segments:
\[
\text{Total Distance} = \text{Area}_A + \text{Area}_B + \text{Area}_C + \text{Area}_D
\]
\[
\text{Total Distance} = 75 + 150 + 200 + 250 = 675 \, \text{meters}
\]
---
Final Answer:
\[
\boxed{675}
\]
Parent Tip: Review the logic above to help your child master the concept of velocity time graphs worksheet.
