# Mechanics, Distance and speed question

1. Mar 31, 2016

### Gajan1234

What is the relationship between the distance y travelled 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.

2. Mar 31, 2016

### Staff: Mentor

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

3. Mar 31, 2016

### Gajan1234

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

4. Mar 31, 2016

### Staff: Mentor

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?

5. Mar 31, 2016

### Gajan1234

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

6. Mar 31, 2016

### Staff: Mentor

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.

7. Mar 31, 2016

### Gajan1234

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

8. Mar 31, 2016

### Staff: Mentor

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

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.)

9. Mar 31, 2016

### Gajan1234

Thank you very much, great mentor!