# Alevel maths help on mechanics question

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#1
https://imgur.com/gallery/iPmI7AS
How do I do this question?

For part a I differentiated v to get acceleration, set this equal to 0 and get t as 0.75 seconds

For part b I set v equal to 0 and get t is 3.5 seconds and then integrated v and subbed in t is 3.5 into this to get -38.79 m is this correct? If not could someone please give some pointers
Last edited by iqraali2002; 1 month ago
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1 month ago
#2
(Original post by iqraali2002)
https://imgur.com/gallery/iPmI7AS
How do I do this question?

For part a I differentiated v to get acceleration, set this equal to 0 and get t as 0.75 seconds

For part b I set v equal to 0 and get t is 3.5 seconds and then integrated v and subbed in t is 3.5 into this to get -38.79 m is this correct? If not could someone please give some pointers
Integrating v from t=0 to 3.5 should be ok. However velocity is +ive in this region, so your distance/displacement should be +ive? Upload what youve done?
Last edited by mqb2766; 1 month ago
0
#3
(Original post by mqb2766)
Integrating v from t=0 to 3.5 should be ok. However velocity is +ive in this region, so your distance/displacement should be +ive? Upload what youve done?
https://imgur.com/gallery/DAYHqVx
This is my working out. Could u check part a and b please?
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1 month ago
#4
(Original post by iqraali2002)
https://imgur.com/gallery/DAYHqVx
This is my working out. Could u check part a and b please?
Seems roughly ok, but do you know why you get a negative displacement for b)?
Also, it would be better to write the definite integral to make the limits clear. If you do an indefinite, you need to include the integration constant.
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#5
(Original post by mqb2766)
Seems roughly ok, but do you know why you get a negative displacement for b)?
Also, it would be better to write the definite integral to make the limits clear. If you do an indefinite, you need to include the integration constant.
Oh okay thanks. I rewrote it using indefinite integral and get 55.46. I see what I did wrong cuz I just ignored the t is -2 solution. Thanks for your help. Would u mind looking at one other mechanics question for me?
Last edited by iqraali2002; 1 month ago
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1 month ago
#6
(Original post by iqraali2002)
Oh okay thanks. I rewrote it using indefinite integral and get 55.46. I see what I did wrong cuz I just ignored the t is -2 solution. Thanks for your help
Err, I think youve made things worse, so my help wasnt that good ..
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#7
(Original post by mqb2766)
Err, I think youve made things worse, so my help wasnt that good ..
Wait where did I go wrong?
https://imgur.com/gallery/lYZpauP
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1 month ago
#8
(Original post by iqraali2002)
Wait where did I go wrong?
https://imgur.com/gallery/lYZpauP
For a definite integral you need ot put the limits on the integral sign, not just bring them in at the end.
The lower limit should be the obvious one when the "simulation" starts.
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#9
(Original post by mqb2766)
For a definite integral you need ot put the limits on the integral sign, not just bring them in at the end.
The lower limit should be the obvious one when the "simulation" starts.
I’m not sure i know what u mean. I don’t understand how my answer is wrong.
When P changes direction of motion is when v is 0. When v is 0 the t values are 3.5 and -2.
Then I integrated v to get distance with the parameters 3.5 and -2
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1 month ago
#10
The question tells you it wants the distance between O and P. O is ...
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#11
(Original post by mqb2766)
The question tells you it wants the distance between O and P. O is ...
Could u do the question and tel me what u get for the distance of P from O at the instant when P changes its direction of motion. In the question it says point O is on the line but it doesn’t specific whether that O is the origin
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1 month ago
#12
(Original post by iqraali2002)
Could u do the question and tel me what u get for the distance of P from O at the instant when P changes its direction of motion. In the question it says point O is on the line but it doesn’t specific whether that O is the origin
Yes it does, at the start. O is the position at time t=0.
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#13
(Original post by mqb2766)
Yes it does, at the start. O is the position at time t=0.
Oh my god I’m an actual idiot okay so O is in the origin so do I divide by answer of 55.46 by 2? Or am I doing it completely wrong?
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1 month ago
#14
(Original post by iqraali2002)
Oh my god I’m an actual idiot okay so O is in the origin so do I divide by answer of 55.46 by 2? Or am I doing it completely wrong?
You integrate velocity from O to P, which is pretty much what you were doing originally.
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#15
(Original post by mqb2766)
You integrate velocity from O to P, which is pretty much what you were doing originally.
And for the upper and lower number on the integral I use 3.5 and 0? To get s is 38.79?
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1 month ago
#16
(Original post by iqraali2002)
And for the upper and lower number on the integral I use 3.5 and 0? To get s is 38.79?
Yes.
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#17
(Original post by mqb2766)
Yes.
Thank you so much. Been stuck on this question for the longest time
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