Finding Acceleration Experimentally

[Power of One]

You drop an object. You take the time it takes to hit the ground. So you have Δx (displacement) and Δx (time).

To find acceleration do you use

xf= xi + Vi t + .5at2
Δ x= Vi t + .5at2
Δ x- Vi t=.5at2
a= 2(Δ x- Vit )/ t2

or do you use

v= Δ x/ Δ t
a= Δ v/ Δ t

Should acceleration come out the same? Why do they differ so much? Take example a Δx of 2m and a time of .5. Using the first equation you get 16 m/s^2. But using the second method, you get 8 m/s^2.

 

[Dale]

Use the first method. The second method is wrong. The key problem is that v=Δx/Δt is an average velocity, not a change in velocity. So you cannot turn around and plug v into the spot for Δv in the second expression. In other words, an average v is not a Δv. In fact, in this case the change in velocity is twice the average velocity (that should not be too surprising) which is where the factor of 2 comes from.

 

[astrokreng]

I would like to clarify that there are different ways to find acceleration experimentally, and both methods mentioned in the question are valid. The first method uses the equation for displacement with constant acceleration, while the second method uses the definition of acceleration as the rate of change of velocity.

It is important to note that both methods rely on accurate measurements of displacement and time. Any errors in these measurements can lead to differences in the calculated acceleration values. Additionally, the first method assumes constant acceleration, which may not always be the case in real-world scenarios. This could also contribute to the differences in the results.

In terms of which method is more accurate, it ultimately depends on the specific experimental setup and the accuracy of the measurements taken. Both methods have their own advantages and limitations. it is important to consider these factors and choose the most appropriate method for each experiment.

In conclusion, while the two methods may yield different results in some cases, they are both valid ways to find acceleration experimentally. It is important to carefully consider the experimental setup and the accuracy of measurements when interpreting the results.