Kinematic Equations: Relationships & Slopes

In summary, the conversation discusses the relationship between velocity and displacement as functions of time, and how these kinematic equations are related to each other. The speaker also mentions the use of graphs and dimensional analysis to understand these concepts. They also explain how the equations can be used to determine an object's velocity at any given time or position.
  • #1
bugsy25
1
0
I'm a little confuse about these.
velocity as a function of time, displacement as a function of time
and velocity as a function of displacement. I know how to use this formulas, but in my lab there is a question that I am stuck on. How are this kinematic equations related to each other? and can you talk about each of their slopes?
 
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  • #2
You take an example in which you once draw graph for velocity constant then the acceleration constant. Looking at the graphs you will understand the things. In fact you can do even dimensional analysis.
 
  • #3
In the equation v = at, which is just from the definition of acceleration, if you assume that you know what the acceleration is, then you can get the final velocity at any time 't.' So we say that we know what v is as a function of time. Likewise, for the equation
v^2= 2 a (x-xo), (assuming here it starts from rest) you can find what an object's velocity is when it is at any position along the x axis. So we say we know velocity as a function of position. If you look up the derivation of this equation, you'll see it comes from basic principles beginning with the first equation and from the definition of average velocity.
 

1. What are the kinematic equations and what do they represent?

The kinematic equations are a set of four equations that describe the relationships between displacement, velocity, acceleration, and time for an object moving with constant acceleration. They represent the mathematical representation of motion for an object.

2. What is the relationship between displacement and time in kinematic equations?

The relationship between displacement and time in kinematic equations is described by the equation: d = v0t + ½at2, where d is displacement, v0 is initial velocity, a is acceleration, and t is time. This equation shows that displacement is directly proportional to time squared, meaning that as time increases, displacement increases at a faster rate.

3. How are velocity and acceleration related in kinematic equations?

The relationship between velocity and acceleration in kinematic equations is described by the equation: v = v0 + at, where v is velocity, v0 is initial velocity, a is acceleration, and t is time. This equation shows that velocity is directly proportional to time, meaning that as time increases, velocity also increases.

4. How can kinematic equations be used to find the slope of a position-time graph?

Kinematic equations can be used to find the slope of a position-time graph by using the equation: v = ∆d/∆t, where v is velocity, ∆d is change in displacement, and ∆t is change in time. The slope of a position-time graph is equal to the velocity of an object at any given point on the graph.

5. Can kinematic equations be used for objects with non-constant acceleration?

Yes, kinematic equations can also be used for objects with non-constant acceleration by using calculus and taking the derivative of the kinematic equations. This allows for the calculation of velocity and acceleration at any given point in time for an object with varying acceleration.

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