Question
Three cars start traveling at the same time the difference the difference traveled by each is represented in three different ways with wide representing miles traveled and t representing time past in hours car one y = t car2 t00 0.20.4 0.6 0.81 y = 00.0004 0.16 0.360.34 and 1 car 3 is a graph starts at 00 and it says y = 2 x - 1 compare the speeds of three cars after 5 hours and your answer describe the function represented by each car
Answers
Answered by
GPT-4o mini
To compare the speeds of the three cars after 5 hours, let's first clarify the functions that represent the distance traveled by each car.
### Car 1
The function for Car 1 is given by:
\[
y = t
\]
This means that the distance traveled by Car 1 (y) is equal to the time (t) in hours. Therefore, after 5 hours:
\[
y = 5 \quad \text{(miles traveled)}
\]
### Car 2
The function for Car 2 is not initially clear from your description, but it seems like you might have meant a piecewise function or specific intervals during which different speeds are maintained. For our purposes, we can interpret the values as:
- At \( t = 0 \), \( y = 0 \)
- At \( t = 0.2 \), \( y = 0.04 \)
- At \( t = 0.4 \), \( y = 0.16 \)
- At \( t = 0.6 \), \( y = 0.36 \)
- At \( t = 0.8 \), \( y = 0.64 \)
- At \( t = 1 \), \( y = 1 \)
From this sequence, we notice that the distances traveled appear to follow a quadratic function approximation:
\[
y = t^2
\]
Calculating the distance after 5 hours would yield:
\[
y = 5^2 = 25 \quad \text{(miles traveled)}
\]
### Car 3
Car 3's function is given by:
\[
y = 2x - 1
\]
After 5 hours, substituting \( x = 5 \):
\[
y = 2(5) - 1 = 10 - 1 = 9 \quad \text{(miles traveled)}
\]
### Summary of Speeds after 5 Hours
- **Car 1** travels **5 miles** after 5 hours, so the speed is \( \frac{5 \text{ miles}}{5 \text{ hours}} = 1 \text{ mph} \).
- **Car 2** travels **25 miles** after 5 hours, so the speed is \( \frac{25 \text{ miles}}{5 \text{ hours}} = 5 \text{ mph} \).
- **Car 3** travels **9 miles** after 5 hours, so the speed is \( \frac{9 \text{ miles}}{5 \text{ hours}} = 1.8 \text{ mph} \).
### Comparison of Speeds
- **Car 1:** 1 mph
- **Car 2:** 5 mph (fastest)
- **Car 3:** 1.8 mph
### Description of Functions
1. **Car 1 (Linear Function)**: The distance traveled is directly proportional to the time, indicating a constant speed of 1 mph.
2. **Car 2 (Quadratic Function)**: The speed increases as time goes on, showcasing a non-linear growth (quadratic growth), which leads to a higher distance traveled after 5 hours.
3. **Car 3 (Linear Function with a Y-Intercept)**: This function also represents constant speed, but starts at -1 which is adjusted. The consistent speed is lower than that of Car 2, but higher than Car 1.
In conclusion, Car 2 is the fastest, followed by Car 3, then Car 1.
### Car 1
The function for Car 1 is given by:
\[
y = t
\]
This means that the distance traveled by Car 1 (y) is equal to the time (t) in hours. Therefore, after 5 hours:
\[
y = 5 \quad \text{(miles traveled)}
\]
### Car 2
The function for Car 2 is not initially clear from your description, but it seems like you might have meant a piecewise function or specific intervals during which different speeds are maintained. For our purposes, we can interpret the values as:
- At \( t = 0 \), \( y = 0 \)
- At \( t = 0.2 \), \( y = 0.04 \)
- At \( t = 0.4 \), \( y = 0.16 \)
- At \( t = 0.6 \), \( y = 0.36 \)
- At \( t = 0.8 \), \( y = 0.64 \)
- At \( t = 1 \), \( y = 1 \)
From this sequence, we notice that the distances traveled appear to follow a quadratic function approximation:
\[
y = t^2
\]
Calculating the distance after 5 hours would yield:
\[
y = 5^2 = 25 \quad \text{(miles traveled)}
\]
### Car 3
Car 3's function is given by:
\[
y = 2x - 1
\]
After 5 hours, substituting \( x = 5 \):
\[
y = 2(5) - 1 = 10 - 1 = 9 \quad \text{(miles traveled)}
\]
### Summary of Speeds after 5 Hours
- **Car 1** travels **5 miles** after 5 hours, so the speed is \( \frac{5 \text{ miles}}{5 \text{ hours}} = 1 \text{ mph} \).
- **Car 2** travels **25 miles** after 5 hours, so the speed is \( \frac{25 \text{ miles}}{5 \text{ hours}} = 5 \text{ mph} \).
- **Car 3** travels **9 miles** after 5 hours, so the speed is \( \frac{9 \text{ miles}}{5 \text{ hours}} = 1.8 \text{ mph} \).
### Comparison of Speeds
- **Car 1:** 1 mph
- **Car 2:** 5 mph (fastest)
- **Car 3:** 1.8 mph
### Description of Functions
1. **Car 1 (Linear Function)**: The distance traveled is directly proportional to the time, indicating a constant speed of 1 mph.
2. **Car 2 (Quadratic Function)**: The speed increases as time goes on, showcasing a non-linear growth (quadratic growth), which leads to a higher distance traveled after 5 hours.
3. **Car 3 (Linear Function with a Y-Intercept)**: This function also represents constant speed, but starts at -1 which is adjusted. The consistent speed is lower than that of Car 2, but higher than Car 1.
In conclusion, Car 2 is the fastest, followed by Car 3, then Car 1.