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secondary 3 | E Maths
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glittr
Glittr

secondary 3 chevron_right E Maths chevron_right Singapore

1) i don’t know if this is a standalone qn but it doesn’t seem to link to the earlier qn
2) no answer is provided

Date Posted: 4 years ago
Views: 331
J
J
4 years ago
What's the part b) and a) like?
Eric Nicholas K
Eric Nicholas K
4 years ago
If the graph is not related to parts a and b, most likely the graph is invalid on the basis that the graphs are not continuous.

For example, just before t = 6, the speed goes down to zero but at t = 6, the speed suddenly increases to 6 m/s without any time interval.

It’s like I am trying to jump off a building and suddenly in 0.001 seconds I find myself falling at terminal velocity.

Hence, the speed time graph would be invalid under this reasoning.
Eric Nicholas K
Eric Nicholas K
4 years ago
There is also an unusual, similar discontinuity at t = 8.

Had the portion after t = 8 come first before the t = 6 to t = 8 portion, the graph would have been a continuous one and would have made sense.
J
J
4 years ago
Not really 0 at t = 6s, but close.

But then many distance time graphs are drawn this way, even though the instantaneous gain/loss in speed as represented by the two kinks on the graph is kind of impossible
Eric Nicholas K
Eric Nicholas K
4 years ago
Whenever I see my students draw out distance time graphs from speed time profiles, I always remind the students to maintain continuity for the graphs because it is unusual for the distance to suddenly spike up or stop. I see a lot of them missing out on continuity during critical transitions.

Even if someone intentionally crashes a vehicle against a wall, the speed time profile would be one that allows a continuous decrease in speed (albeit for a extremely short time interval) rather than a sudden change in speed.
J
J
4 years ago
The graduations on the time axis are perhaps too large. It could be that short interval continuous decrease you mentioned (maybe milli/microseconds kind) but they appear to be kinks here due to the scale.

But I would give the answer along the same lines of impossible instantaneous decrease/increase if I were Unicorn

Edit : the graph could be correct if the object moving has the ability to carry out extremely quick acceleration (eg. Sports car)
J
J
4 years ago
It's not actually accurate to say the graph has discontinuity as there are no gaps

https://www.math24.net/discontinuous-functions/

Examples of impossible time graphs :

https://slideplayer.com/slide/3873810/

http://www.shodor.org/interactivate/discussions/ImpossibleGraphs/
Eric Nicholas K
Eric Nicholas K
4 years ago
Perhaps it’s better to say that the graph is not differentiable at those points.

Or the derivative graph of the function graph is discontinuous.
glittr
Glittr
4 years ago
thanks everyone for their input . i will ask the qn setter for the ans and post here in future

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glittr
Glittr's answer
59 answers (Tutor Details)
1st
hi Eric , when u said if it would make sense if the portion from t=8 onwards is swapped with the portion t=6 to 8 , do u mean like in this new diagram ? Also , is it possible for the OLDER qn to involve a ferrari that suddenly increases speed ?
Eric Nicholas K
Eric Nicholas K
4 years ago
Perfect! Yes this is what I meant by a good continuous flow.
Eric Nicholas K
Eric Nicholas K
4 years ago
For the Ferrari example, even if the Ferrari accelerates sharply, there is that tiny period of time for which there car has to undertake in order to increase its speed. The graph would not fit the Ferrari’s motion of rapid acceleration, but would be very very close.
glittr
Glittr
4 years ago
thanks for explaining