Kinematics derivation: what's "ds/dv" ?

In summary, the conversation discusses a derivation for an equation in Uniform Accelerated Motion (UAM) and the significance of ds/dv in the derivation. The equation is often expressed as a = dv/dt = dv/ds * ds/dt = v * dv/ds, where dv/ds represents the rate of change of speed with respect to distance. However, ds/dv does not hold much importance in the overall interpretation of the equation.
  • #1
Taulant Sholla
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5
Hello, here's a derivation for one of the equations for Uniform Accelerated Motion (UAM). I like it because it's far more concise than the algebra version. Question though: is there any kind of meaningful interpretation of ds/dv (which starts everything off in step 1)? Thank you!

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  • #2
The derivation is usually done as follows: $$a=\frac{dv}{dt}=\frac{dv}{ds}\frac{ds}{dt}=v\frac{dv}{ds}$$where dv/ds is the rate of change of speed with respect to distance. So ds/dv is the reciprocal of dv/ds, but it doesn't have much fundamental significance.
 
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Likes Charles Link
  • #3
Very helpful. Thank you so much!
 

1. What is "ds/dv" in kinematics derivation?

"ds/dv" refers to the derivative of position (s) with respect to velocity (v). It is a measure of how much the position changes with a change in velocity, and is often used in kinematics equations to calculate acceleration.

2. How is "ds/dv" calculated?

The calculation of "ds/dv" involves taking the derivative of the position function with respect to velocity. This can be done using the basic rules of differentiation, such as the power rule and chain rule.

3. What is the significance of "ds/dv" in kinematics?

"ds/dv" is an important concept in kinematics as it represents the relationship between position and velocity. It is used to calculate acceleration, which is a key component in understanding the motion of objects.

4. Can "ds/dv" have a negative value?

Yes, "ds/dv" can have a negative value. This indicates that the position and velocity are changing in opposite directions. For example, if an object is slowing down, its velocity is decreasing while its position is increasing, resulting in a negative "ds/dv" value.

5. How does "ds/dv" relate to other kinematics variables?

"ds/dv" is related to other kinematics variables such as acceleration, velocity, and displacement through equations such as a = ds/dv and v = ds/dt. It helps to describe the relationship between these variables and how they change over time.

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