Question 1199443: The distance covered by a rolling object at intervals of 1 second were recorded as 4 cm, 16 cm, 28 cm, 40 cm, etc. After how long will the object be 22.6m from the starting point?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
Every 1s, the rolling object moves 12cm, therefore it has a speed of 12cm/s, and no acceleration.
speed = distance/time
solving for time:
time = distance/speed
Divide 22.6m (2260cm) by 12cm/s to get the amount of time to travel 22.6m.
You should get a value that is a little more than 3 minutes.
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While tutor Ikleyn's solution is fine, given her explanation and interpretation of the first second (nonuniform motion), the problem does not say that the rolling object started from rest. Thus, one can also assume (as I did) that at the t=0 instant, the object was already rolling at 12cm/sec. With this assumption, we get 2260/12 = 188.33 sec. Again, it all depends on how one interprets the starting condition, and the problem as worded leaves it open to interpretation.
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Oops, disregard my "explanation" -- I realize now that the 4cm is what is non-uniform, and yes, that piece must be ignored temporarily as the distances after that are all 12cm apart, then the initial "piece" of 4cm (+1 sec) needs to be added back in. Duh! Good catch Ikleyn!
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
The distance covered by a rolling object at intervals of 1 second were recorded
as 4 cm, 16 cm, 28 cm, 40 cm, etc. After how long will the object be 22.6m
from the starting point?
~~~~~~~~~~~~~~~~~
I interpret the given distances as the distances from the starting point
at the time moments t= 1s, 2s, 3s, 4s and so on.
Notice that  first second the increment of the distance
from the starting point is the same: it is 12 cm for every 1 second.
So, we can assume that after first second the movement is uniform with the constant speed of 12 cm/s.
(Without making this assumption, we can not answer the question, at all).
Ok. But if consider the movement from the starting time moment t= 0,
the movement IS NOT UNIFORM.
So, in order for the solution be correct, we should consider time interval AFTER 1 second: t >= 1 second.
Under this consideration, the object will cover the distance from the mark of 4 cm
to the mark of 22.6 m (= 2260 cm) in
 = 188 seconds.
To answer the problem's question, I must add 1 second to 188 seconds
to account for the very first second and very first 4 cm.
So, the ANSWER is 1 + 188 = 189 seconds.
Solved.
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Surely, it can be solved in many different ways, but ALL SUCH SOLUTIONS
must account for the fact that the movement is not uniform in whole.
It is uniform (or can be assumed uniform) only AFTER first second.
This problem is to check and to train attentiveness of a student.
In other words, the problem has a huge underwater stone (a trap),
and the meaning of a solution is to recognize this trap and to avoid falling in it.
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