Three cars start traveling at the same time. The distance traveled by each is represented in three different ways, with y representing miles traveled and t representing time passed in hours.

Question

Car 1:
y=t

Car 2: T 0, 0.2, 0.4, 0.6, 0.8, 1
y=t^2 0, 0.04, 0.16, 36.0, 64.0, 1

Car 3:the numbers on the graph show 1 to 5 on the X and Y axis,a curving line on the graph starts from zero curving infinitely upwards on the grapgh near the number 5, this curve is y=2t - 1

Answer 1

Let's break down the information you provided about the three cars in terms of the equations and the data points associated with each car.

Car 1:

The distance traveled by Car 1 is given by the equation: \[ y = t \] This means Car 1 travels a distance equal to the time in hours, in miles.

Car 2:

The distance traveled by Car 2 is represented by the equation: \[ y = t^2 \] The provided data points for Car 2 are:

• \( t = 0 \) hours: \( y = 0^2 = 0 \) miles
• \( t = 0.2 \) hours: \( y = (0.2)^2 = 0.04 \) miles
• \( t = 0.4 \) hours: \( y = (0.4)^2 = 0.16 \) miles
• \( t = 0.6 \) hours: \( y = (0.6)^2 = 0.36 \) miles
• \( t = 0.8 \) hours: \( y = (0.8)^2 = 0.64 \) miles
• \( t = 1 \) hour: \( y = (1)^2 = 1 \) mile

This shows that Car 2 travels a distance equal to the square of the time elapsed.

Car 3:

The equation for Car 3 is given as: \[ y = 2t - 1 \] This is a linear equation. To compute the distance traveled at different times, you can use the formula. For example:

• When \( t = 0 \): \( y = 2(0) - 1 = -1 \) miles (not realistic since distance can't be negative, it indicates that the car is likely still gaining speed or not in motion until a certain time)
• When \( t = 1 \): \( y = 2(1) - 1 = 1 \) mile
• When \( t = 2 \): \( y = 2(2) - 1 = 3 \) miles
• When \( t = 3 \): \( y = 2(3) - 1 = 5 \) miles
• Continue incrementally for larger \( t \) values.

Comparing the Cars:

• Car 1 travels linearly, meaning it has a constant speed of 1 mile per hour.
• Car 2 travels at an increasing rate, as the distance is the square of the time, leading to greater distances over time.
• Car 3 travels in a linear manner but starts at -1 mile (could be interpreted as needing to accelerate before starting to accumulate distance), and subsequently increases distance linearly as time increases.

To visualize their speeds:

• Car 1 has a speed of 1 mile per hour.
• Car 2 initially starts slow but accelerates quickly.
• Car 3 also has a linear growth but with a smaller base speed.

In conclusion, depending on the time \( t \), you can analyze who travels the farthest or the fastest among the three cars based on their respective equations.