Adding two lines, what is the equation of the new line?

In summary, the conversation discusses finding an equation relating the speed of a vehicle and the overall distance it takes to stop. The equations for speed versus thinking distance and speed versus braking distance are given, and there is a question about finding an equation for speed versus overall distance using these equations. The conversation also includes a suggestion to use different variables to represent the different distances and a comment about adding two lines. The issue is eventually resolved.
  • #1
saplingg
26
0

Homework Statement



Basically I was given a table displaying speed of a vehicle, thinking distance (distance it takes for driver to react) and braking distance. I am told to find an equation relating speed of vehicle and overall distance (overall distance = thinking distance + braking distance).



The Attempt at a Solution



Using graphing software, I've managed to find an approximate equation relating speed and thinking distance, as well as an equation relating speed and braking distance.

The equations are :

For speed vs thinking dist., y = (16/3)x, where y is speed of vehicle and x is thinking distance
and
For speed vs braking dist., y = 13(x^0.5), where y is the speed of vehicle and x is braking distance



Is there any way I can find an equation for speed versus overall distance using these 2 equations that I've obtained?
 
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  • #2
saplingg said:
Is there any way I can find an equation for speed versus overall distance using these 2 equations that I've obtained?
Sure. It might be more obvious if you didn't use the same letter to denote thinking distance and braking distance.

(And shouldn't those constants have some units on them?)
 
  • #3
Could anyone show me how?

@Hurkyl: I used subscripts to distinguish the distances
 
  • #4
You are talking about the TOTAL distance aren't you?

(And you titled this "ADDING two lines"!)
 
  • #5
yeah what is wrong with that?
 
  • #6
Err It's ok, I've solved it. Thanks to all who read
 

What is the equation for the new line?

The equation for the new line can be found by using the point-slope form of a line, which is y - y1 = m(x - x1). In this case, you will use the slope of the two given lines and the coordinates of any point on the new line to determine the equation.

Can the new line be parallel or perpendicular to the given lines?

Yes, the new line can be parallel or perpendicular to the given lines, depending on the slopes of the two given lines. If the slopes are equal, the new line will be parallel to the given lines. If the slopes are negative reciprocals of each other, the new line will be perpendicular to the given lines.

Is there a specific method for adding two lines?

Yes, there are a few methods for adding two lines. One method is by finding the slope and y-intercept of each line, then using the point-slope form of a line to determine the equation of the new line. Another method is by graphing the two lines and finding the coordinates of the point where they intersect, then using the coordinates to determine the equation of the new line.

Do the two lines have to be in the same plane to be added?

Yes, in order to add two lines, they must be in the same plane. This means that they must lie on the same flat surface and not intersect each other at any point.

Can the new line intersect with one of the given lines?

Yes, the new line can intersect with one of the given lines. This will occur when the two given lines have different slopes and intersect at a point. In this case, the new line will also pass through that point of intersection.

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