Experiment Help: Investigating Freely Falling Bodies

[bilalbajwa]

Experiment Help!

Homework Statement

We were given this experiment in which we have to investigate the motion of a freely falling body on a fictitious planet.

2. Things we have to do
(1) the value of the acceleration due to gravity on the planet, (sucessfully did it)
(2) how the distance fallen depends on the elapsed time, and
(3) an interesting relation between the instantaneous velocity at the center of a time interval and the average velocity over that interval.

Can anybody explain me what will be the conclusion of the part (2)
and part (3).

 

[husky88]

Is there friction at the surface of the planet?
Assuming there isn't, you can still use the vector kinematics formulas.
For example, you can think about
d = vo*t + 1/2 a t^2

 

[andrevdh]

Can you give us more information on what measurements were given?

 

[dontdisturbmycircles]

Since acceleration is constant, your acceleration vs time graph will look like this :

Since acceleration is constant, the velocity changes at a constant rate every second and thus the velocity time graph is ALWAYS linear under constant acceleration like so:

Note: these images are not to scale with each other.

For number 3, what is the equation for the midpoint of a line, can you you use this relationship to find an interesting equation for the relationship between the initial velocity, the final velocity, and the average velocity under constant acceleration?

A little bit of extra information since I made these graphs anyway, I want to show you another interesting relationship.

You probably notice that the distance traveled is the area under a velocity/time graph?

If you tried to compute the area of a portion of the velocity-time graph I drew you would come up with the following equation:

For the red area, the area is $$v_{o}*t$$ and for the bluish area the area can be found by $$\frac{1}{2}(v_{f}-v_{o})*t$$

Which can be combined to form $$d=\frac{(v_{f}-v_{o})*t}{2}+\frac{2v_{o}*t}{2}$$ which is equal to $$d=\frac{(v_{f}+v_{o})*t}{2}$$ which is a well known kinematics equation that you probably use ;-).

I added this in because you seem to enjoy developing a good understanding of physics in the other threads and the solution to #3 of your problem is very similar.

 

[bilalbajwa]

Thanks a lot for reply and this wonderfull equation relationship!
Please be tune i am going to show u a lab experiment!

 

[dontdisturbmycircles]

Did you get #2 and #3 solved?