To compare the speeds of the three cars after 5 hours and describe the functions, let's analyze each car based on the information given.
Car 1:
The function represented is \( y = t \). This indicates that the distance traveled (y in miles) is equal to the time spent traveling (t in hours). Therefore, after 5 hours: \[ y = 5 \implies \text{Distance traveled by Car 1} = 5 , \text{miles} \] The speed of Car 1 can be calculated as: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{5}{5} = 1 , \text{mile per hour} \]
Car 2:
The data points for Car 2 are as follows (assuming these are representative of \( t \) values and their corresponding distances traveled):
- 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 \( t = 1 \): \( y = 1 \)
Noticing the pattern, we can see that this appears to represent the function: \[ y = t^2 \] This means the distance increases with the square of time. After 5 hours: \[ y = (5)^2 = 25 , \text{miles} \] The speed of Car 2 is therefore: \[ \text{Speed} = \frac{25}{5} = 5 , \text{miles per hour} \]
Car 3:
Since a description for Car 3 wasn't provided, we generally assume a car would also follow a linear or quadratic path like the first two. However, assuming typical function paths for the context, we could hypothesize that it might resemble constant speed \( y = kt \) where \( k \) adheres to constant mileages, or a quadratic function like Car 2. Without specific details, we cannot compute the distance or speed of Car 3.
Summary of Car Speeds After 5 Hours:
- Car 1 travels 5 miles at 1 mile per hour (linear function \( y = t \)).
- Car 2 travels 25 miles at 5 miles per hour (quadratic function \( y = t^2 \)).
- Car 3: Unknown without specific details.
If Car 3 can be represented as either being a constant speed or another quadratic function, more information would be needed to conclude accurately.
Based on this data, Car 2 is the fastest, car 1 is the slowest, and conclusions for Car 3 depend on further information.