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Normanhurst Boys Questions (1 Viewer)

scaryshark09

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for 9, i knew it was C or D
when i differentiated the velocity function, it was positive, so doesnt that mean speed is increased
i also tested similar time points and the velocity seemed to be increasing.
but the answer is D somehow

for 4, i have no idea
 

user18181818

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for 9 if u differentiate it you get 6costsint and then sub 5pi/6 in that it's negative - therefore D
what's the answer to 4?
 
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scaryshark09

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for 9 if u differentiate it you get 6cost and then sub 5pi/6 in that it's negative - therefore D
what's the answer to 4?
the derivative is 6costsint and yes i know that its negative when you sub in, but that doesn't mean that the speed is decreasing, that just means that the speed is in the negative direction
 

scaryshark09

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i understand 4 now (C), but can someone explain why the speed is decreasing in question 9?
 

scaryshark09

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Like @user18181818 said, the derivative is 6cosxsinx and if you substitute t=5π/6, you get -2.5980.... which is decreasing speed since the gradient is negative, thus, D.
i disagree.
that doesnt mean that the speed is decreasing
 

scaryshark09

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Like @user18181818 said, the derivative is 6cosxsinx and if you substitute t=5π/6, you get -2.5980.... which is decreasing speed since the gradient is negative, thus, D.
that just means the speed is in the negative direction, but that doesnt matter for thisn question as speed is a scalar quantity. you have to differentiate again to find the gradiant of the speed to find out if its increasing or decreasing. and this is positive. so shouldnt the answer be C?
 

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that just means the speed is in the negative direction, but that doesnt matter for thisn question as speed is a scalar quantity. you have to differentiate again to find the gradiant of the speed to find out if its increasing or decreasing. and this is positive. so shouldnt the answer be C?
As you said you have to differentiate again. This gives you the acceleration which is positive, also as you said. A positive acceleration means the particle is being pushed to the right, while a negative velocity means the particle is moving to the left. Since it is moving to the left but being pushed to the right, it is slowing down
 

scaryshark09

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Screen Shot 2023-10-19 at 9.34.35 pm.pngScreen Shot 2023-10-19 at 9.34.46 pm.png
how come they divide by 2 in part (i) but not (ii)??
 

scaryshark09

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can someone explain when and when not to divide by 2?
and why do you even need to divide by 2?
if theres 12 people in a line, and you choose 6, how is this double the answer? @carrotsss
 

carrotsss

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can someone explain when and when not to divide by 2?
and why do you even need to divide by 2?
if theres 12 people in a line, and you choose 6, how is this double the answer? @carrotsss
It’s the same deal as last time, for each possibility you also have an identical possibility with the groups swapped, so in order to cancel this out you halve it. the reason part 2 is different is because there are 2 people who have been fixed in one group and hence there is never an identical possibility where everyone’s in the other group because they’re never in the other group themselves
 

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