Question

Hi, I would like to know which method should we use when doing physics calculations?

Acceleration = Speed / Time

Let's say we are given 5 measurements of speed and time. S1, S2, S3, S4, S5 and T1,T2,T3,T4,T5.

We are given two methods.

1) Find the mean of speed and time, and find their respective standard deviation and standard error. E.g. speed = 0.5 +- 0.2 m/s and 3 +- 0.2 s, substituting into the acceleration formula and doing the respective uncertainties combinations/

or 2) Find the acceleration of each set e.g. (S1, T1), (S2,T2).... After which we find the mean acceleration from the 5 newly calculated results, standard deviation and standard error?

Answer 1

Hey when doing these type of physics calculations like trying to figure out the mean acceleration of 5 measurements of speed and time the method 2 will be the correct way.....ie. find acceleration of each measurement and then take it's mean to find the mean acceleration.

Reason : Let's take like 5 measurements of speed as s1,s2,s3,s4,s5 and time as t1,t2,t3,t4,t5.

We know that acceleration in measurememt 1 (a1) comes out be s1/t1 and similarly a2 , a3 ,a4 ,a5 will be s2/t2,s3/t3,s4/t4 and s5/t5.

So now we have found out the acceleration of the object under each iteration of the experiment and taking the mean of these accelerations will give us the mean acceleration of the object . The process goes by the like the definition of acceleration and will give us the right result.

Approach 1 is wrong because we are having the speed and time measurements of the same object under 5 measurements and we need to find the mean acceleration ie. The mean of accelerations under each iteration while by approach 1 we'll be doing ::: mean of speed of all measurements / mean of time which will be some value of acceleration totally unrelated to the acceleration of the object in each iteration of the experiment.

Hence, Approach 2 is the correct approach!

Hope it helps.

Your feedback is greatly appreciated!