Further maths Maths Kinematics

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Pepushka
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How would you go about doing these questions . I be been doing suvat equations but can’t seem to get the right answers .
3) A particle accelerates from rest at a constant rate of 3 ms^-2 up to speed of Vms^-1 it continues to move for a certain time then desiderates at a constant rate of 1.5 ms^-2 until it comes to rest given that the total time taken is one minute and the total distance travelled is 1 km find the value of V .
5)a particle is projected upwards vertically from point A . given that it rises 15 m in the third second of its motion find its initial speed and the maximum height reached above A .
6) A particle P1 is projected vertically upwards from the horizontal ground with a speed of 30ms^-1 at the same instant another particle P2 is projected vertically upwards from the top of a tower of height 25 m with a speed of 10ms^-1
Find :
i) The time for which P1 is higher than the top of the tower
ii) The velocity is of the particles of the instant when the particles are at the same height
iii) The time for which P1 is higher than P2 and is moving upwards
7) two trains are waiting at the station. The first train leaves the station at time T is equal to 0 and accelerated 0.3ms^-2. The second train is 10 seconds later and accelerate at 0.5ms^-2.How fast are the trains moving at the point when the next level with each other?
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Pepushka
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mqb2766
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(Original post by Pepushka)
How would you go about doing these questions . I be been doing suvat equations but can’t seem to get the right answers .
3) A particle accelerates from rest at a constant rate of 3 ms^-2 up to speed of Vms^-1 it continues to move for a certain time then desiderates at a constant rate of 1.5 ms^-2 until it comes to rest given that the total time taken is one minute and the total distance travelled is 1 km find the value of V .
5)a particle is projected upwards vertically from point A . given that it rises 15 m in the third second of its motion find its initial speed and the maximum height reached above A .
6) A particle P1 is projected vertically upwards from the horizontal ground with a speed of 30ms^-1 at the same instant another particle P2 is projected vertically upwards from the top of a tower of height 25 m with a speed of 10ms^-1
Find :
i) The time for which P1 is higher than the top of the tower
ii) The velocity is of the particles of the instant when the particles are at the same height
iii) The time for which P1 is higher than P2 and is moving upwards
7) two trains are waiting at the station. The first train leaves the station at time T is equal to 0 and accelerated 0.3ms^-2. The second train is 10 seconds later and accelerate at 0.5ms^-2.How fast are the trains moving at the point when the next level with each other?
It's generally best to do/post one question at a time.
Can you post what you tried for 3? Usually a sketch helps (perhaps velocity-time) as well as writing down clearly which suvat variables you know/need to find and potential suvat equations.
Last edited by mqb2766; 1 year ago
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Pepushka
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mqb2766
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(Original post by Pepushka)
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Can you draw the velocity - time graph more clearly?
There are a few similar ways to solve it, but it's important to get the relationship between v and time in the acceleration/constant velocity/deceleration phases. The main equation to determine v is obviously the distance travelled which corresponds to the area under the velocity-time graph.

Note you have 3 suvat (simple) phases here. The trick is to join them together and write the total distance travelled equation in terms of a single variable, v.

Note it's generally better to post on the maths - f38 forum.
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Pepushka
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(Original post by mqb2766)
Can you draw the velocity - time graph more clearly?
There are a few similar ways to solve it, but it's important to get the relationship between v and time in the acceleration/constant velocity/deceleration phases. The main equation to determine v is obviously the distance travelled which corresponds to the area under the velocity-time graph.

Note you have 3 suvat (simple) phases here. The trick is to join them together and write the total distance travelled equation in terms of a single variable, v.

Note it's generally better to post on the maths - f38 forum.
Thank you so much redrawing the graph more clearly actually really helped me and I managed to get the answer properly this time . What is the f38 forum ?
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mqb2766
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(Original post by Pepushka)
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Thank you so much redrawing the graph more clearly actually really helped me and I managed to get the answer properly this time . What is the f38 forum ?
It's just about always worth drawing a graph/sketching the information for a suvat question. Helps you get the ideas straiight. Can you do it for 5), it's really just a quadratic, vertical distance-time question. If not, upload what you've tried.

The maths forum (f38) is
https://www.thestudentroom.co.uk/forumdisplay.php?f=38
Last edited by mqb2766; 1 year ago
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