The equation for the motion of the faster car can be written as:
y = mx + b
where y represents the distance in miles and x represents the time in hours. To find the equation, we need to determine the values of m and b.
On Road 1, the car can go 60 miles in 2 hours. This gives us one set of coordinates: (2, 60).
On Road 2, the car can go 90 miles in 4 hours. This gives us another set of coordinates: (4, 90).
We can now use these coordinates to find the slope, m, and the y-intercept, b.
The slope, m, can be calculated using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the values from Road 1, we have:
m = (60 - 0) / (2 - 0) = 60 / 2 = 30
Substituting the values from Road 2, we have:
m = (90 - 0) / (4 - 0) = 90 / 4 = 22.5
We can see that the car on Road 1 is faster since it covers 30 miles in 1 hour, while the car on Road 2 covers 22.5 miles in 1 hour.
Now, let's find the y-intercept, b.
Using the coordinates of Road 1, we can substitute the values (2, 60):
y = mx + b
60 = 30(2) + b
60 = 60 + b
b = 60 - 60
b = 0
Using the coordinates of Road 2, we can substitute the values (4, 90):
y = mx + b
90 = 22.5(4) + b
90 = 90 + b
b = 90 - 90
b = 0
Since both equations have a y-intercept of 0, the equation representing the motion of the faster car is:
y = 30x
Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y is the distance in miles and x is the time in hours to represent the motion of the faster car.
3 answers
which of these objects is moving at a rate of 2 feet per second
To determine which object is moving at a rate of 2 feet per second, we need more information about the objects in question. Without any additional context, it is not possible to determine which object is moving at a rate of 2 feet per second.
1 answer