# Mechanics M2 - Variable Acceleration (Vectors)Watch

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Thread starter 5 years ago
#1
I need help with an M2 question on variable acceleration (vectors). Here is the question: At time t seconds (t》0), a particle P is moving in a plane with acceleration a=(5t-3)i+(8-t)j. When t=0, the velocity of P is (2i-5j)ms^-1. Find the value of t for which P is moving parallel to i-j. Could someone help me out please?
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5 years ago
#2
First, you're given some useful information about the velocity, so you might want to start off by finding v, noting that

and not forgetting the constant of integration (a vector which you can then find using the info).

Let me know when you've done that
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Thread starter 5 years ago
#3
(Original post by Indeterminate)
First, you're given some useful information about the velocity, so you might want to start off by finding v, noting that

and not forgetting the constant of integration (a vector which you can then find using the info).

Let me know when you've done that
Hey there, I did that and got: v= (2.5t^2-3t+2)i+(8t-0.5t^2-5)j ms^-1. I'm not sure what to do next though.
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5 years ago
#4
(Original post by 123456789012)
Hey there, I did that and got: v= (2.5t^2-3t+2)i+(8t-0.5t^2-5)j ms^-1. I'm not sure what to do next though.
The key now is to think of what it means for it to be parallel to i-j. The direction i-j i.e is where the j component is the negative of the i component. Use this to solve for t
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Thread starter 5 years ago
#5
(Original post by Indeterminate)
The key now is to think of what it means for it to be parallel to i-j. The direction i-j i.e is where the j component is the negative of the i component. Use this to solve for t
That's exactly what I don't know! I would know what to do if the question told me the particle was moving parallel to i or j only. However, I'm unsure on how to go about doing this question.
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5 years ago
#6
(Original post by 123456789012)
That's exactly what I don't know! I would know what to do if the question told me the particle was moving parallel to i or j only. However, I'm unsure on how to go about doing this question.
The word 'parallel' means that it's travelling in the same direction as the vector i-j at some time, t.

Note the characteristic of i-j is that the j component is the negative of the i component, which defines the direction of it.

So, you must set up an equation so that the vector v conforms to this definition.

Can you do it now?
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5 years ago
#7
(Original post by 123456789012)
I need help with an M2 question on variable acceleration (vectors). Here is the question: At time t seconds (t》0), a particle P is moving in a plane with acceleration a=(5t-3)i+(8-t)j. When t=0, the velocity of P is (2i-5j)ms^-1. Find the value of t for which P is moving parallel to i-j. Could someone help me out please?
Integrate the acceleration to get the velocity then put equal to K(i-j) where k is a constant.
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Thread starter 5 years ago
#8
(Original post by brianeverit)
Integrate the acceleration to get the velocity then put equal to K(i-j) where k is a constant.
Thanks a lot! That makes sense! You've helped me out a lot.
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