A car starts driving at noon (t = 0) and drives at exactly 50 miles per hour until 4pm (t = 4). (a) How far does the car drive in that time? (b) Sketch a graph of the car's speed (in miles per hour) vs its time (in hours). Shade in the area below your graph, between t = 0 and t = 4.
A car starts driving at noon (t = 0) and drives at exactly 50 miles per hour until 4pm (t = 4). (a) How far does the car drive in that time? (b) Sketch a graph of the car's speed (in miles per hour) vs its time (in hours). Shade in the area below your graph, between t = 0 and t = 4.
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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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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![### Problem Statement on Constant Speed Driving
**1. A car starts driving at noon (t = 0) and drives at exactly 50 miles per hour until 4 pm (t = 4).**
**(a) How far does the car drive in that time?**
*Solution:*
To determine the distance driven, use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
In this case, the speed is 50 miles per hour, and the time is 4 hours (from noon to 4 pm).
\[ \text{Distance} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{miles} \]
So, the car drives **200 miles** during this time period.
**(b) Sketch a graph of the car’s speed (in miles per hour) vs its time (in hours). Shade in the area below your graph, between t = 0 and t = 4.**
*Explanation:*
The graph of the car's speed vs time is a horizontal line because the speed is constant at 50 miles per hour. The x-axis represents the time (t) in hours, and the y-axis represents the speed (s) in miles per hour.
**Drawing the Graph:**
1. Draw the time axis (horizontal) from \( t = 0 \) to \( t = 4 \).
2. Draw the speed axis (vertical) up to at least 50 miles per hour.
3. Plot a horizontal line at \( y = 50 \) from \( t = 0 \) to \( t = 4 \).
**Shaded Area:**
The area below the line (from \( t = 0 \) to \( t = 4 \)) and above the time axis represents the distance traveled. Since the car drives at a constant speed:
\[
\text{Shaded Area} = \text{Speed} \times \text{Time} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{square units}
\]
This visual representation confirms that the car covers 200 miles.
**Graph Details:**
- The x-axis is labeled "Time (hours)" ranging from 0 to 4.
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b645cb8-b8df-4c84-bb3a-c321bbb71008%2F50919e1d-5f54-401e-ad50-e043bcf121a5%2Fy67nbr_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement on Constant Speed Driving
**1. A car starts driving at noon (t = 0) and drives at exactly 50 miles per hour until 4 pm (t = 4).**
**(a) How far does the car drive in that time?**
*Solution:*
To determine the distance driven, use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
In this case, the speed is 50 miles per hour, and the time is 4 hours (from noon to 4 pm).
\[ \text{Distance} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{miles} \]
So, the car drives **200 miles** during this time period.
**(b) Sketch a graph of the car’s speed (in miles per hour) vs its time (in hours). Shade in the area below your graph, between t = 0 and t = 4.**
*Explanation:*
The graph of the car's speed vs time is a horizontal line because the speed is constant at 50 miles per hour. The x-axis represents the time (t) in hours, and the y-axis represents the speed (s) in miles per hour.
**Drawing the Graph:**
1. Draw the time axis (horizontal) from \( t = 0 \) to \( t = 4 \).
2. Draw the speed axis (vertical) up to at least 50 miles per hour.
3. Plot a horizontal line at \( y = 50 \) from \( t = 0 \) to \( t = 4 \).
**Shaded Area:**
The area below the line (from \( t = 0 \) to \( t = 4 \)) and above the time axis represents the distance traveled. Since the car drives at a constant speed:
\[
\text{Shaded Area} = \text{Speed} \times \text{Time} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{square units}
\]
This visual representation confirms that the car covers 200 miles.
**Graph Details:**
- The x-axis is labeled "Time (hours)" ranging from 0 to 4.
-
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