A plot of velocity versus time for a car for the first 15 seconds of motion is shown in the diagram below. The distance traveled during these 15 seconds is: v, m/s 30 20 10 300 m 30 m 375 m 75 m 450 m 5 10 1 15 t, s
A plot of velocity versus time for a car for the first 15 seconds of motion is shown in the diagram below. The distance traveled during these 15 seconds is: v, m/s 30 20 10 300 m 30 m 375 m 75 m 450 m 5 10 1 15 t, s
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Velocity vs. Time Analysis**
A plot of velocity versus time for a car for the first 15 seconds of motion is shown in the diagram below. The distance traveled during these 15 seconds is:
**Diagram Explanation:**
- The graph is a velocity-time graph, displaying velocity (v) on the vertical axis in meters per second (m/s) and time (t) on the horizontal axis in seconds (s).
- The graph consists of two segments:
- From t = 0 to t = 5 seconds, the velocity increases linearly from 0 m/s to 30 m/s.
- From t = 5 to t = 15 seconds, the velocity remains constant at 30 m/s.
**Distance Calculation Options:**
- ○ 300 m
- ○ 30 m
- ○ 375 m
- ○ 75 m
- ○ 450 m
To find the total distance traveled, calculate the area under the velocity-time graph.
- **Triangle (0 to 5 s):** \[\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 30 = 75 \, \text{m}\]
- **Rectangle (5 to 15 s):** \[\text{Area} = \text{base} \times \text{height} = 10 \times 30 = 300 \, \text{m}\]
**Total Distance:** 75 m + 300 m = 375 m
Thus, the correct answer is ○ 375 m.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2F21799ee8-f7db-4513-a44c-2771520043be%2F72r7auf_processed.png&w=3840&q=75)
Transcribed Image Text:**Velocity vs. Time Analysis**
A plot of velocity versus time for a car for the first 15 seconds of motion is shown in the diagram below. The distance traveled during these 15 seconds is:
**Diagram Explanation:**
- The graph is a velocity-time graph, displaying velocity (v) on the vertical axis in meters per second (m/s) and time (t) on the horizontal axis in seconds (s).
- The graph consists of two segments:
- From t = 0 to t = 5 seconds, the velocity increases linearly from 0 m/s to 30 m/s.
- From t = 5 to t = 15 seconds, the velocity remains constant at 30 m/s.
**Distance Calculation Options:**
- ○ 300 m
- ○ 30 m
- ○ 375 m
- ○ 75 m
- ○ 450 m
To find the total distance traveled, calculate the area under the velocity-time graph.
- **Triangle (0 to 5 s):** \[\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 30 = 75 \, \text{m}\]
- **Rectangle (5 to 15 s):** \[\text{Area} = \text{base} \times \text{height} = 10 \times 30 = 300 \, \text{m}\]
**Total Distance:** 75 m + 300 m = 375 m
Thus, the correct answer is ○ 375 m.
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