Formula help needed algebraic formula for intra-interval rate of acceleration

In summary, the conversation is about finding an algebraic formula for calculating the average acceleration between spreadsheet intervals, given that the intra-interval rate of acceleration is constant and the speeds at the beginning and end of the interval are known. The desired formula should not involve derivatives or trigonometric functions and should take into account the exponential increase in acceleration within the interval. The correct formula for acceleration is the change in speed divided by the change in time between two time intervals.
  • #1
seasnake
42
0
This isn't for a class, just for my own personal use as I am not a student, but I need an equation in algebraic form that allows me to calculate the average acceleration between spreadsheet intervals given that the intra-interval rate of acceleration is to be treated as a constant, and the speed at the beginning of the interval is known and the speed at the end of the interval is also known.

T = time
Speed at T = 4 is 6
Speed at T = 5 is 4
Speed at T = 6 is 7
Speed at T = 7 is 7

I am searching for an algebraic formula (non-derivitative, non-trig) that gives the average rate of intra-interval acceleration if the rate of intra-interval acceleration were constant between T = 5 and T = 6. Speed at T = 4 and speed at T =7 should have no impact to this intra-interval multiplier.

Said another way, I have a spreadsheet and I have formulated it so that the average rate of interval acceleration between T = 5 and T = 6 is (Speed at T = 5 + Speed at T = 6)/2, but I know that this is incorrect as the intra-interval rate should rise exponentially between T = 5 and T = 6, so instead of multiplying by 0.5 I should be multiplying by a different fraction that is exponentially related.
 
Last edited:
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  • #2
Acceleration is change of speed per time step, not average velocity during the time step.
So the acceleration between time T and T' is
[(speed at T') - (speed at T)] / (T' - T)
 
  • #3
Since this is not "Linear and Abstract Algebra", I am moving it to "General Math".
 
Last edited by a moderator:

What is an intra-interval rate of acceleration?

An intra-interval rate of acceleration refers to the change in acceleration of an object over a specific time interval. It is typically denoted as "a" and measured in meters per second squared (m/s²).

Why do we need an algebraic formula for intra-interval rate of acceleration?

An algebraic formula allows us to calculate the exact value of the intra-interval rate of acceleration for a given situation. This can be useful in physics and engineering applications where precise measurements and calculations are necessary.

What is the algebraic formula for intra-interval rate of acceleration?

The formula for intra-interval rate of acceleration is given by:
a = (v₂ - v₁) / (t₂ - t₁)
where a is the acceleration, v₂ and v₁ are the final and initial velocities, and t₂ and t₁ are the final and initial times, respectively.

Can the formula for intra-interval rate of acceleration be used for all types of motion?

Yes, the formula can be used for any type of motion, whether it is linear, circular, or any other type. However, it is important to use the correct values for velocity and time in the formula depending on the type of motion being analyzed.

How can the algebraic formula for intra-interval rate of acceleration be applied in real-life situations?

The formula can be used in various real-life situations, such as calculating the acceleration of a car during a certain time interval, or determining the acceleration of a projectile in physics experiments. It can also be used to analyze the performance of athletes, machines, and other moving objects.

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