Mechanics, Distance and speed question

[Gajan1234]

What is the relationship between the distance y traveled by an object falling freely from rest and the time x the object has been falling?

The answer to this question is: y is proportional to x2

Can someone tell me how this answer is correct.

 

[Doc Al]

Are you familiar with the kinematics of falling bodies? (An example of constant acceleration motion.)

 

[Gajan1234]

Are you familiar with the kinematics of falling bodies? (An example of constant acceleration motion.)

Yes, I understand that but I still do not understand why it is X^2. Can you please explain and thank you.

 

[Doc Al]

Yes, I understand that but I still do not understand why it is X^2.

They are just using, for some strange reason, "X" to stand for the time. Is that the concern?

Can you write the kinematic equation for distance as a function of time?

 

[Gajan1234]

They are just using, for some strange reason, "X" to stand for the time. Is that the concern?

Can you write the kinematic equation for distance as a function of time?

s=ut+at^2/2 and s=(u+v)/2 x t there is a lot more

 

[Doc Al]

s=ut+at^2/2

That's the one you need. Since the object is falling from rest, what is u? And change the standard variable names to what they want in the problem, Y and X.

 

[Gajan1234]

That's the one you need. Since the object is falling from rest, what is u? And change the standard variable names to what they want in the problem, Y and X.

Thank you indeed but last question: why do we reject the other equations.
and also even if I make the initial velocity zero, then I would end up with 2s=at^2, t

 

[Doc Al]

Thank you indeed but last question: why do we reject the other equations.

Only because we want an equation that links distance to time. The other equations link other variables, so they won't help us here.

and also even if I make the initial velocity zero, then I would end up with 2s=at^2,

Sure, you end up with s=at^2/2 = (a/2)t^2.

Which tells you that the distance fallen is proportional to the square of the time. (You can replace s with y, and t with x, to make it match the variable names used in the problem statement.)

 

[Gajan1234]

Thank you very much, great mentor!