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M2 help please

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Sgrafitti
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#1
Report Thread starter 11 years ago
#1
A particle P of mass 0.2 kg is at rest at a fixed origin O. At time t seconds, where 0 \leq t \leq 3 , is a force (2ti + 3j)N applied to P.

a) Find the position vector of P when t = 3.

I worked this out without a problem.

r = 45i +67.5j

b) When t = 3, the force acting on P changes to (6i + (12 - t^2)j)N, where t \geq 3. Find the velocity of P when t = 6.

No idea to go with this one. Could anyone give me any idea?

I got as far as v = 30ti + (60t - \frac{5}{3} t^3)j+ c

Don't know how I'd work out C. Thanks in advance for helping me out.
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rbnphlp
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#2
Report 11 years ago
#2
(Original post by Sgrafitti)
A particle P of mass 0.2 kg is at rest at a fixed origin O. At time t seconds, where 0 \leq t \leq 3 , is a force (2ti + 3j)N applied to P.

a) Find the position vector of P when t = 3.

I worked this out without a problem.

r = 45i +67.5j

b) When t = 3, the force acting on P changes to (6i + (12 - t^2)j)N, where t \geq 3. Find the velocity of P when t = 6.

No idea to go with this one. Could anyone give me any idea?

I got as far as v = 30ti + (60t - \frac{5}{3} t^3)j+ c

Don't know how I'd work out C. Thanks in advance for helping me out.
F=ma
you have m and F , find a
a=\frac{dv}{dt}
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Adam_Smithers
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#3
Report 11 years ago
#3
(Original post by rbnphlp)
F=ma
you have m and F , find a
a=\frac{dv}{dt}
Huh? I've got to find the velocity. I found the acceleration and I've integrated it, leaving the answer I have in part b). I just don't know how to find C. :sigh:
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Trevor 12345
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#4
Report 11 years ago
#4
(Original post by Sgrafitti)
A particle P of mass 0.2 kg is at rest at a fixed origin O. At time t seconds, where 0 \leq t \leq 3 , is a force (2ti + 3j)N applied to P.

a) Find the position vector of P when t = 3.

I worked this out without a problem.

r = 45i +67.5j

b) When t = 3, the force acting on P changes to (6i + (12 - t^2)j)N, where t \geq 3. Find the velocity of P when t = 6.

No idea to go with this one. Could anyone give me any idea?

I got as far as v = 30ti + (60t - \frac{5}{3} t^3)j+ c

Don't know how I'd work out C. Thanks in advance for helping me out.
Well assuming that you did (a) correctly then you know that the answer will be found by using calculus...
the steps to your problems are along the lines of
(i) find the acceleration as other poster mentioned.
(ii) integrate/ solve the D.E. to give you the velocity function in terms of time (+C of course)
(iii) Now the problem is that you do not have the boundary conditions needed to find the +C (but you will have in a minute)
(iv) you now need to use the F provided in part (a) to find the velocity function for part (a) and then use this to see what the velocity was at 6 seconds.
(v) Use you info from part (iv) i,e, when t=6, v= ___ to find the value of you r missing C from step (ii) ...( C will of course be a vector)
(vi) should be easy now....
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Trevor 12345
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#5
(Original post by Sgrafitti)
A particle P of mass 0.2 kg is at rest at a fixed origin O. At time t seconds, where 0 \leq t \leq 3 , is a force (2ti + 3j)N applied to P.

a) Find the position vector of P when t = 3.

I worked this out without a problem.

r = 45i +67.5j

b) When t = 3, the force acting on P changes to (6i + (12 - t^2)j)N, where t \geq 3. Find the velocity of P when t = 6.

No idea to go with this one. Could anyone give me any idea?

I got as far as v = 30ti + (60t - \frac{5}{3} t^3)j+ c

Don't know how I'd work out C. Thanks in advance for helping me out.
Well assuming that you did (a) correctly then you know that the answer will be found by using calculus...
the steps to your problems are along the lines of
(i) find the acceleration as other poster mentioned.
(ii) integrate/ solve the D.E. to give you the velocity function in terms of time (+C of course)
(iii) Now the problem is that you do not have the boundary conditions needed to find the +C (but you will have in a minute)
(iv) you now need to use the F provided in part (a) to find the velocity function for part (a) and then use this to see what the velocity was at 6 seconds.
(v) Use you info from part (iv) i,e, when t=6, v= ___ to find the value of you r missing C from step (ii) ...( C will of course be a vector)
(vi) should be easy now....
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Adam_Smithers
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#6
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#6
(Original post by Mrm.)
Well assuming that you did (a) correctly then you know that the answer will be found by using calculus...
the steps to your problems are along the lines of
(i) find the acceleration as other poster mentioned.
(ii) integrate/ solve the D.E. to give you the velocity function in terms of time (+C of course)
(iii) Now the problem is that you do not have the boundary conditions needed to find the +C (but you will have in a minute)
(iv) you now need to use the F provided in part (a) to find the velocity function for part (a) and then use this to see what the velocity was at 6 seconds.
(v) Use you info from part (iv) i,e, when t=6, v= ___ to find the value of you r missing C from step (ii) ...( C will of course be a vector)
(vi) should be easy now....
Thanks.
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Trevor 12345
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#7
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(Original post by Adam_Smithers)
Thanks.
No problem old bean.
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splitter2017
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#8
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#8
Surely acceleration has to be constant to use suvat in order to get s = 45i + 67.5j This is not so!
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niamhdoesmaths
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#9
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#9
(Original post by splitter2017)
Surely acceleration has to be constant to use suvat in order to get s = 45i + 67.5j This is not so!
Hey This is an extremely old thread! I'm sure they don't need help from 8 years in the future, so I'm going to close this thread due to age
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