Find 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 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.

 

[Vykan12]

It seems to me that you're not given enough information. If you had the initial and final velocity, you could plug into

$$V_{f} = V_{i} + at$$

to experimentally find the acceleration.

What would be easier is to use Newton's second law (F=ma) since then you only need to know the object's mass and the force it exerts on the ground upon impact to experimentally determine the value of g.

 

[tomcue]

I would like to clarify that both methods are correct and can be used to find acceleration experimentally. However, the first equation (xf= xi + Vi t + .5at2) is more accurate as it takes into account the initial velocity (Vi). The second equation (a= Δ v/ Δ t) assumes that the initial velocity is zero, which may not be the case in all scenarios.

In the example given, the difference in the values of acceleration obtained using the two equations is due to the initial velocity (Vi) being ignored in the second equation. This can significantly affect the accuracy of the results, especially for larger displacement and time values.

To ensure the most accurate results, it is important to consider all relevant variables, including initial velocity, in the equations used to find acceleration experimentally. Both equations are valid, but the first one provides a more comprehensive and accurate approach.