Motion on incline

1. Oct 7, 2006

Cole07

problem: A ball is allowed to roll from rest down an inclined plane, and the distances are marked every 2.5s. if the second mark is made 1.5m from the starting point, where is the first mark?

where is the fourth mark?

well i made a velocity vs. t chart and the velocity of it is 0.6 then ifound the velocity of ech number on my graph but iwas told my answer was wrong. can you help me please.

Last edited: Oct 7, 2006
2. Oct 7, 2006

3. Oct 7, 2006

Cole07

how this is only my second time?

4. Oct 7, 2006

Cyrus

There is a thread for homework help on the main page. It's the second one down from the top.

5. Oct 7, 2006

arildno

Let indices 1,2 indicate different instants and the associated distances travelled. Thus, using your distance formula for two different times, we've got the formulae:
$$d_{1}=\frac{a}{2}t_{1}^{2} (1), d_{2}=\frac{a}{2}t_{2}^{2}(2)$$
where a is the acceleration.

Now, divide these equations with each other:
$$\frac{d_{1}}{d_{2}}=\frac{\frac{a}{2}t_{1}^{2}}{\frac{a}{2}t_{2}^{2}}\to\frac{d_{1}}{d_{2}}=\frac{t_{1}^{2}}{t_{2}^{2}}\to$$
$$\frac{d_{1}}{d_{2}}=(\frac{t_{1}}{t_{2}})^{2}$$

agreed?

6. Oct 7, 2006

Cole07

i'm sorry i don't understand any of that

7. Oct 7, 2006

arildno

Nonsense.
Start studying it from line 1, and report back precisely what you don't understand!

8. Oct 7, 2006

Cole07

where do you get 1,2

9. Oct 7, 2006

arildno

I give two NAMES to two different instants!!
Am I not allowed to give names to quantities?

Should I give them the same name, perhaps??

10. Oct 7, 2006

Cole07

so the 1st equation would be 1.5=a(2.5)^2 right?

11. Oct 7, 2006

arildno

If you want $t_{1}$ to be interpreted as 2.5, yes.

12. Oct 7, 2006

Cole07

ok for this i get 0.24, but what is the second instants the fourth mark?

13. Oct 7, 2006

arildno

Look, do you understand how I got the equation:
$$\frac{d_{1}}{d_{2}}=(\frac{t_{1}}{t_{2}})^{2}$$

14. Oct 7, 2006

Cole07

not really, i do understand the 1,2 now but i don't see where you get the second instants. this problem just really confuses me i'm sorry.

15. Oct 7, 2006

arildno

Do you understand that I can divide one equation with the other?

16. Oct 7, 2006

Cole07

so you took d=a(t)^2 and divided it by itself? with different subscripts?

17. Oct 7, 2006

Cole07

so you took d=a(t)^2 and divided it by itself to get D(1)/D(2)=(t(1)/t(2))^2 right?

18. Oct 7, 2006

Cole07

sorry i didn't see it come up i typed it again ignore the first on please.

19. Oct 7, 2006

arildno

Correct!
Do you agree I am allowd to do that?

20. Oct 7, 2006

Cole07

yes, but is the first instants the first mark and the second instants the second mark?