Question about speed distance and time

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Cambridge101

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Why is it on a distance time graph for example, where there is a constant speed shown, does any point on the line represent a distance that in % terms, is equally as far up the x-axis as is the y-axis.

For example, say i travel 50km per hour. Therefore, every 5 km i travel takes 6 minutes. Therefore, every 0.83 recurring miles I travel, takes 1 minute. Now, both 0.83 recurring and 1 minute both represent 1.6 recurring % of their axes distance. 0.83miles recur is 1.6 rec % of 50miles and 1 min is 1.6 rec % of 60 mins. So the point (1,0.83) on the line is in terms of %, is as far up the miles axis as it is the time axis. I cant seem to find a intuitive way to understand this. The reason I want to, is because if I am told i travel 50km per hour, and I travel just 10km. I know that 10km is 20% of 50km, therefore 20% up the miles axis (y-axis). Thus assuming what I just said is true, the time taken to go 10km must also be 20% of the time axis, which is 0.2*60 = 12. This makes out that at a speed of 50kmph I can travel 10km in 12 mins. So I can travel a distance 20% of the 50 mile in a time 20% of the 60 min. Im sorry if this is hard to understand, I cannot put it into words any other way.
 
Cambridge101 said:
Why is it on a distance time graph for example, where there is a constant speed shown, does any point on the line represent a distance that in % terms, is equally as far up the x-axis as is the y-axis.

For example, say i travel 50km per hour. Therefore, every 5 km i travel takes 6 minutes. Therefore, every 0.83 recurring miles I travel, takes 1 minute. Now, both 0.83 recurring and 1 minute both represent 1.6 recurring % of their axes distance. 0.83miles recur is 1.6 rec % of 50miles and 1 min is 1.6 rec % of 60 mins. So the point (1,0.83) on the line is in terms of %, is as far up the miles axis as it is the time axis. I cant seem to find a intuitive way to understand this. The reason I want to, is because if I am told i travel 50km per hour, and I travel just 10km. I know that 10km is 20% of 50km, therefore 20% up the miles axis (y-axis). Thus assuming what I just said is true, the time taken to go 10km must also be 20% of the time axis, which is 0.2*60 = 12. This makes out that at a speed of 50kmph I can travel 10km in 12 mins. So I can travel a distance 20% of the 50 mile in a time 20% of the 60 min. Im sorry if this is hard to understand, I cannot put it into words any other way.
Click to expand...
D=VT
D1 = VT1

D1/D = (VT1)/(VT) = T1/T
 
Cambridge101 said:
i do not really understand your explanation too well sir...
Click to expand...
You noted in your example that 10km is the same % of 50km as 12min of 60min. Same % means same ratio. I showed that with constant speed the ratios of distances and corresponding times are always the same.
 
lev888 said:
You noted in your example that 10km is the same % of 50km as 12min of 60min. Same % means same ratio. I showed that with constant speed the ratios of distances and corresponding times are always the same.
Click to expand...
Sorry this still is not clear to me. Can you please explain another way?
 
lev888 said:
Yes. 10/50 = 12/60
Click to expand...
yes. This is what I found to be the case, but why is this the case. If i am travelling 50km every 60 min, i am therefore travelling 10 km every 12 min. This implies that if i travel 20% of the distance, i travel also 20% of the time. Intuitively i cant see why this is always the case for constant velocity.
 
Cambridge101 said:
yes. This is what I found to be the case, but why is this the case. If i am travelling 50km every 60 min, i am therefore travelling 10 km every 12 min. This implies that if i travel 20% of the distance, i travel also 20% of the time. Intuitively i cant see why this is always the case for constant velocity.
Click to expand...
Post #2 explains why. If speed is constant we get the result in post #2.
 
Cambridge101 said:
Hmmm....this is not helping me man, so sorry.
Click to expand...
[imath]v = \dfrac{d}{t}[/imath] for any d and t. So if we are traveling a distance [imath]d_1[/imath] we do it with a time determined by [imath]v = \dfrac{d_1}{t_1}[/imath]. Similarly for a distance and time at the same speed [imath]d_2,~t_2 \implies v = \dfrac{d_2}{t_2}[/imath]. So know that
[imath]v = \dfrac{d_1}{t_1} = \dfrac{d_2}{t_2}[/imath]

Rearranging we get
[imath]\dfrac{d_1}{d_2} = \dfrac{t_1}{t_2}[/imath]
as lev888 has been saying.

-Dan
 
topsquark said:
[imath]v = \dfrac{d}{t}[/imath] for any d and t. So if we are traveling a distance [imath]d_1[/imath] we do it with a time determined by [imath]v = \dfrac{d_1}{t_1}[/imath]. Similarly for a distance and time at the same speed [imath]d_2,~t_2 \implies v = \dfrac{d_2}{t_2}[/imath]. So know that
[imath]v = \dfrac{d_1}{t_1} = \dfrac{d_2}{t_2}[/imath]

Rearranging we get
[imath]\dfrac{d_1}{d_2} = \dfrac{t_1}{t_2}[/imath]
as lev888 has been saying.

-Dan
Click to expand...
Either is this, could you please explain maybe using words.
 
Reminder of what I am asking:

Why is it on a distance time graph for example, where there is a constant speed shown, does any point on the line represent a distance that in % terms, is equally as far up the x-axis as is the y-axis.

For example, say i travel 50km per hour. Therefore, every 5 km i travel takes 6 minutes. Therefore, every 0.83 recurring miles I travel, takes 1 minute. Now, both 0.83 recurring and 1 minute both represent 1.6 recurring % of their axes distance. 0.83miles recur is 1.6 rec % of 50miles and 1 min is 1.6 rec % of 60 mins. So the point (1,0.83) on the line is in terms of %, is as far up the miles axis as it is the time axis. I cant seem to find a intuitive way to understand this. The reason I want to, is because if I am told i travel 50km per hour, and I travel just 10km. I know that 10km is 20% of 50km, therefore 20% up the miles axis (y-axis). Thus assuming what I just said is true, the time taken to go 10km must also be 20% of the time axis, which is 0.2*60 = 12. This makes out that at a speed of 50kmph I can travel 10km in 12 mins. So I can travel a distance 20% of the 50 mile in a time 20% of the 60 min. Im sorry if this is hard to understand, I cannot put it into words any other way.
 
Cambridge101 said:
Reminder of what I am asking:

Why is it on a distance time graph for example, where there is a constant speed shown, does any point on the line represent a distance that in % terms, is equally as far up the x-axis as is the y-axis.

For example, say i travel 50km per hour. Therefore, every 5 km i travel takes 6 minutes. Therefore, every 0.83 recurring miles I travel, takes 1 minute. Now, both 0.83 recurring and 1 minute both represent 1.6 recurring % of their axes distance. 0.83miles recur is 1.6 rec % of 50miles and 1 min is 1.6 rec % of 60 mins. So the point (1,0.83) on the line is in terms of %, is as far up the miles axis as it is the time axis. I cant seem to find a intuitive way to understand this. The reason I want to, is because if I am told i travel 50km per hour, and I travel just 10km. I know that 10km is 20% of 50km, therefore 20% up the miles axis (y-axis). Thus assuming what I just said is true, the time taken to go 10km must also be 20% of the time axis, which is 0.2*60 = 12. This makes out that at a speed of 50kmph I can travel 10km in 12 mins. So I can travel a distance 20% of the 50 mile in a time 20% of the 60 min. Im sorry if this is hard to understand, I cannot put it into words any other way.
Click to expand...
Since you are talking about distance time graphs, let's make one.
Draw the coordinate plane and a line through the origin. Pick a point on the line. Draw a vertical line from the point to the time (x) axis. See a triangle? Its leg lengths are time and distance values.
Pick another point and draw a vertical line. See the second triangle?
The 2 triangles are similar. Therefore, ratios of corresponding sides are the same.
 
lev888 said:
Since you are talking about distance time graphs, let's make one.
Draw the coordinate plane and a line through the origin. Pick a point on the line. Draw a vertical line from the point to the time (x) axis. See a triangle? Its leg lengths are time and distance values.
Pick another point and draw a vertical line. See the second triangle?
The 2 triangles are similar. Therefore, ratios of corresponding sides are the same.
Click to expand...
How does this help me understand why then, the base of the triangle is the same percentage of the total length of the x-axis as the opposite side is a % of the total length of y-axis?
 
Cambridge101 said:
How does this help me understand why then, the base of the triangle is the same percentage of the total length of the x-axis as the opposite side is a % of the total length of y-axis?
Click to expand...
Total length of the x-axis? No. We are considering ratios of sides of 2 triangles. 10 to 50, 12 to 60.
 
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