How Far Did a Ball Travel in the First 5 Seconds of Uniform Acceleration?

[Tehy]

I'm learning physics and I'm now working on with one line motion problems and I'm jammed with this one problem:

A ball starts from rest and rolls down a hill with uniform accelration, traveling 150m during the second 5.0s of it's motion. How far did it roll during the first 5.0s of motion?

I just can't figure out how to solve this. Could someone help me?

Thanks!

 

[prasannapakkiam]

This sounds like a homework question.

Anyway:
http://www.physchem.co.za/Graphs/Equations.htm
The 4 Basic linear Equations of Motion can help.

Hint:
-Use s=ut+(at^2)/2 & v=u+at
-Find a
Then use s=ut+(at^2)/2

If you need more help post at the Homework Questions section.

 

[Tehy]

Yeah, I have tried those equations, but I can't get the right answer...

 

[arunbg]

Please post how you worked out the problem, so that we may point out the errors.

 

[Tehy]

Please post how you worked out the problem, so that we may point out the errors.

Well, I'll try :) So ball starts from rest, so Xo = 0, Vox = 0, T1 = 0. Then the ball rolls 5s and it's place is X1 and V1x = ?. Finally the ball rolls the second 5s and then X2 = X1 + 150m, V2x = ? and T2 = 10s


When the ball rolls first 5s:
(1) X1 = 1/2(AxT1^2)

The ball rolls second 5s (from X1 to X2):
(2) X2 = X1 + V1xt + 1/2(AxT2^2)

Then I combine those equations (1) and (2), but with no luck.

 

[arunbg]

You should also write V1 in terms of the acceleration A.
Eliminate all other unknowns except A, remember you have values for X2, T1 and T2.

 

[prasannapakkiam]

Correct me if I may be wrong.

df=distance in first 5s
t=5 in all cases

df=ut+(at^2)/2
since: v=u+at
therefore:df=(0+at)t+(25a)/2
therefore:150=37.5a

 

[arunbg]

Yes, you are correct and I hope the OP has understood the solution.