Kinematic equations and their applications

In summary, the kinematic equations are valid for any motion undergoing constant or zero acceleration and can be applied to any time interval. The initial and final velocities, as well as the time, should correspond to the specific time interval being analyzed. However, there may be situations where certain liberties can be taken with the equations, such as in a gravity field. It is important to understand how to apply the equations in different situations and not forget about any necessary terms.
  • #1
fishingspree2
139
0
Hello,

I have a question concerning the kinematic equations

http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L6a1.gif

vi and vf stand for initial and final velocity, my question is: do these velocities need to be the initial (t=0) and final (end of the motion)?

can't I just use two velocities in the motion, even if its not initial and final?

I have the same question for the t.. does the t value need to be calculated from t=0?

sorry for my bad english
 
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  • #2
These equations are valid for any motion undergoing constant acceleration (or zero acceleration). They are good for any time interval. The vi and vf need to correspond to the initial and final values of velocity for any time interval you are interested in examining. So, no, you do not need to begin your analysis at t=0, but often it is convenient to do this.
 
  • #3
fishingspree2 said:
Hello,

I have a question concerning the kinematic equations


vi and vf stand for initial and final velocity, my question is: do these velocities need to be the initial (t=0) and final (end of the motion)?

can't I just use two velocities in the motion, even if its not initial and final?

I have the same question for the t.. does the t value need to be calculated from t=0?

sorry for my bad english

You can take certain liberties with the equations in a gravity field because say the time to max height is equal to the time falling from max height if originally at rest.

But a more useful approach is understanding how to apply them in various situations and not to forget about the terms that may apply depending on the situation. For instance the d= ... equation may at times have an initial d that needs to be accounted for but isn't in the equation you show.
 

FAQ: Kinematic equations and their applications

What are the basic kinematic equations?

The basic kinematic equations are:
1. v = u + at (velocity equation)
2. s = ut + 0.5at^2 (displacement equation)
3. v^2 = u^2 + 2as (velocity squared equation)
4. s = (u + v)t/2 (average velocity equation)
5. a = (v-u)/t (acceleration equation)
where v is final velocity, u is initial velocity, a is acceleration, t is time, and s is displacement.

How do I use kinematic equations to solve problems?

To use kinematic equations to solve problems, follow these steps:
1. Identify the known and unknown variables in the problem.
2. Choose the appropriate kinematic equation based on the given information.
3. Substitute the known values into the equation.
4. Solve for the unknown variable.
5. Check your answer for accuracy and units.

What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time taken, while instantaneous velocity is the velocity at a specific moment in time. Average velocity gives an overall picture of an object's motion, while instantaneous velocity gives information about an object's velocity at a specific point in time.

Can I use kinematic equations for any type of motion?

Kinematic equations can be used for any type of motion as long as the acceleration is constant. This means that the velocity and acceleration do not change during the motion. If the acceleration is not constant, more advanced equations and mathematical techniques may be required to solve the problem.

How do I know when to use positive or negative values in kinematic equations?

In kinematic equations, positive values are used for motion in the positive direction, and negative values are used for motion in the negative direction. It is important to choose a consistent direction throughout the problem. If the values for displacement, velocity, or acceleration are given with a direction, use that direction to determine whether it is positive or negative. If no direction is given, you can choose arbitrarily, but it is important to be consistent throughout the problem.

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