Kinematic Equation vs. Delta velocity / Delta Time - Factor of 2?

In summary, the conversation discusses a problem comparing the kinematic equation and a standard change in velocity over change in time to determine acceleration. The speaker's derivation shows that the kinematic equation is exactly 2 times that of delta v/ delta time. The conversation also includes a suggestion that the issue may be due to using average velocity instead of instantaneous velocity, which can result in a factor of 2 difference. The speaker also clarifies that the average velocity for uniform acceleration is equal to the sum of the initial and final velocity divided by 2.
  • #1
JeremyAdrian
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0
I am testing a cylindrical piece of steel dropping down steel pipe in a vacuum system, and came across a problem comparing the kinematic equation and a standard change in velocity over change in time to determine an acceleration. My derivation shows that the kinematic equation is exactly 2 times that of delta v/ delta time.

I have attached my calculations. Has anyone came across this issue before?

It is driving me crazy! Thanks for the help.
 

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  • Kinematic Eq vs Delta vel over delta time.pdf
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  • #2
Ah, because (d2-d1)/(t2-t1) gives you average velocity between t1 and t2. Not the instantaneous velocity at t2, which is what you need for your formula to work. If object is at rest at t1, under uniform acceleration, velocity at t2 will be exactly twice the average velocity between t1 and t2. That might be the factor of 2 you are looking for.
 
  • #3
Realize that (d2-d1)/(t2-t1) is the average velocity between t1 and t2. It's not the the speed at time t2.

The average velocity (for uniform acceleration) = (Vi + Vf)/2.
 

1. What is the difference between the kinematic equation and the delta velocity/delta time equation?

The kinematic equation is a mathematical formula that relates an object's displacement, velocity, and acceleration. It is a general equation that can be used to solve various kinematics problems. On the other hand, the delta velocity/delta time equation is a specific formula that calculates an object's average velocity by dividing the change in its velocity by the change in time.

2. Why is there a factor of 2 in the delta velocity/delta time equation?

The factor of 2 in the delta velocity/delta time equation comes from the definition of average velocity. Average velocity is calculated by dividing the change in position by the change in time. However, in the case of delta velocity/delta time, we are interested in the average velocity over a specific time interval, which is half of the total time interval. Therefore, we need to divide the change in velocity by half of the total time interval, which is equivalent to multiplying by a factor of 2.

3. How is the kinematic equation related to the delta velocity/delta time equation?

The kinematic equation is a general equation that can be derived from the delta velocity/delta time equation. By rearranging the delta velocity/delta time equation, we can obtain the kinematic equation for an object with constant acceleration: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time interval.

4. Can the delta velocity/delta time equation be used for objects with non-constant acceleration?

No, the delta velocity/delta time equation can only be used for objects with constant acceleration. For objects with non-constant acceleration, the kinematic equation or other more advanced kinematics equations must be used.

5. What are some real-life applications of the kinematic equation and the delta velocity/delta time equation?

The kinematic equation and the delta velocity/delta time equation are widely used in physics and engineering to solve problems related to motion. They can be applied to various real-life situations, such as calculating the speed of a falling object, determining the displacement of a moving car, or predicting the trajectory of a projectile. These equations are also essential in fields like robotics, aerospace engineering, and sports science.

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