Mechanics help

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Kffh
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#1
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#1
1) A particle P moves in a straight line. At time t s the displacement s cm from a
fixed point O is given by s = 1/6 ( 8 t 3 - 105 t 2 + 144 t + 540 ) . Find the distance between the points at which the particle is instantaneously at rest.
2) A particle P moves along a straight line. Initially, P is at rest at a point O on the line. At time t s, the velocity of P is v ms^(-1), where v=1/20(5-t)^(2), 0<(or equal to)t<(or equal to)8.
a) Sketch a velocity time graph for the motion of P
b) Find the values of t and the corresponding values of v when the acceleration of P is instantaneously zero.
I am struggling a lot with this and would appreciate in depth explanations with working outs to help me understand. Thankyou
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Tayls102
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#2
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#2
for (1), You have an equation for the displacement of the particle at time t. Do you know how displacement and velocity are related? If a particle is at rest, what would it's velocity be?

for (2): you are given an equation for the velocity v, at time t. part a is asking you to sketch this relation, are you comfortable with sketching graphs?
for part b, its asking you a question about acceleration, do you know how acceleration and velocity are related (similar to (1))?

just getting a feel of what you are and aren't comfortable with so i can help better
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Kffh
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#3
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(Original post by Tayls102)
for (1), You have an equation for the displacement of the particle at time t. Do you know how displacement and velocity are related? If a particle is at rest, what would it's velocity be?

for (2): you are given an equation for the velocity v, at time t. part a is asking you to sketch this relation, are you comfortable with sketching graphs?
for part b, its asking you a question about acceleration, do you know how acceleration and velocity are related (similar to (1))?

just getting a feel of what you are and aren't comfortable with so i can help better
When a particle is at rest it’s velocity would be zero and acceleration is the change in velocity per time I believe. I can sketch the graphs but I’m a bit confused with this specific one
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Tayls102
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#4
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#4
okay so for (1) we need to find the points where the velocity is 0. So first we need to find an expression for velocity, velocity is the rate of change of displacement, or in other words ds/dt. Once you have found this, you can set it to 0 to find the times where the velocity is 0. Have you got any working so far which you could post?

(2) part b is similar to the above, except you want times where acceleration is 0. remember that acceleration is the rate of change of velocity, so dv/dt.


Sketching graphs:
If you follow these steps for sketching graphs it shouldn't matter what type of function you have.

1) Find the x and y intercepts, if any exist.
2) Find any stationary points of the curve, determine their location and their nature (max/min etc)
3) Determine the behaviour of the curve towards +/- infinity, and find any asymptotes of the curve (if any).

Have a go at sketching it and if you get stuck i can help.
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Kffh
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#5
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(Original post by Tayls102)
okay so for (1) we need to find the points where the velocity is 0. So first we need to find an expression for velocity, velocity is the rate of change of displacement, or in other words ds/dt. Once you have found this, you can set it to 0 to find the times where the velocity is 0. Have you got any working so far which you could post?

(2) part b is similar to the above, except you want times where acceleration is 0. remember that acceleration is the rate of change of velocity, so dv/dt.


Sketching graphs:
If you follow these steps for sketching graphs it shouldn't matter what type of function you have.

1) Find the x and y intercepts, if any exist.
2) Find any stationary points of the curve, determine their location and their nature (max/min etc)
3) Determine the behaviour of the curve towards +/- infinity, and find any asymptotes of the curve (if any).

Have a go at sketching it and if you get stuck i can help.
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This is how far I’ve gotten for the first one, should I just subtract the 2 distances now?
Last edited by Kffh; 2 years ago
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Tayls102
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(Original post by Kffh)
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This is how far I’ve gotten for the first one, should I just subtract the 2 distances now?
yeh this looks good, yeh the difference between these distances is just the absolute value of the difference of the two distances.
One thing I would add to your working is how you got to t=8,3/4. I.e show the factorisation or the use of the quadratic formula.
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Kffh
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#7
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(Original post by Tayls102)
yeh this looks good, yeh the difference between these distances is just the absolute value of the difference of the two distances.
One thing I would add to your working is how you got to t=8,3/4. I.e show the factorisation or the use of the quadratic formula.
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Here is my working for q2, not sure if it’s correct
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Tayls102
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(Original post by Kffh)
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Here is my working for q2, not sure if it’s correct
would you be able to screenshot the equation for v? from the one in the question I'm not sure if its the right one or not, v=(1/20)(5-t)2?
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Kffh
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#9
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(Original post by Kffh)
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Here is my working for q2, not sure if it’s correct
(Original post by Tayls102)
would you be able to screenshot the equation for v? from the one in the question I'm not sure if its the right one or not, v=(1/20)(5-t)2?
Here
Attached files
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Tayls102
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#10
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Okay, double check your expanded expression for v, i think you might have made a slip up somewhere. If you post how you got to v=(1/4)t-(1/20)v3.
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Kffh
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#11
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#11
(Original post by Tayls102)
Okay, double check your expanded expression for v, i think you might have made a slip up somewhere. If you post how you got to v=(1/4)t-(1/20)v3.
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Size:  155.4 KBRealised my mistake, hope this looks better
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Tayls102
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#12
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#12
The maths looks good, and the shape of your curve looks good to. For the graph there's a few things I'd mention:

- Remember to label both axes, i know it seems trivial but its easy marks to lose.
- Make sure to label the stationary points with both their x and y values.
- For this particular question, you only need to sketch the graph for 0<t<8. It might be worth calculating the value of the graph at t=8 and noting this on the graph just so you have the full picture.
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Kffh
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#13
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(Original post by Tayls102)
The maths looks good, and the shape of your curve looks good to. For the graph there's a few things I'd mention:

- Remember to label both axes, i know it seems trivial but its easy marks to lose.
- Make sure to label the stationary points with both their x and y values.
- For this particular question, you only need to sketch the graph for 0<t<8. It might be worth calculating the value of the graph at t=8 and noting this on the graph just so you have the full picture.
Will do, thanks!!!
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Tayls102
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#14
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(Original post by Kffh)
Will do, thanks!!!
no worries, are you okay with the other parts of the question?
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Kffh
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#15
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#15
(Original post by Tayls102)
no worries, are you okay with the other parts of the question?
Yes thankyou
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DarkShadow101
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#16
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are you not supposed to use integration from the values t=8 and t=3/4?
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davros
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#17
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(Original post by DarkShadow101)
are you not supposed to use integration from the values t=8 and t=3/4?
This thread is 9 months old now, but why would you need to use integration when you are given the displacement formula as part of the question?
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