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    I'm trying to do some revision before classes start again tomorrow but I'm struggling a little bit with this one, any help would be greatly appreciated! I've included my working so far:

    A particle moves in 2D with a vector velocity which at time t is ' v = (-0.4ti + 5j) m/s '.


    At time t=0 the particle is at (3,2)

    a) Find the acceleration vector at time t

    b) Find the position vector at time t

    c) Find the speed at time t = 10




    I found the acceleration vector at time t to be -0.4i m/s^2


    I can't figure out how to find the position vector at time t and also not sure how I'd carry on to do part c.


    I've integrated to get: 'r = -0.2t²i + 5tj + c' and i know at time t=0, 'r = 3i + 2j' but I'm not sure what to do to finish off the question. Thank you for any help! I know I have to substitute it in to find c, but I think I'm being a little silly and I'm not sure how to sub in and solve, when t is still in the first equation :confused:
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    (Original post by chris35)
    I've integrated to get: 'r = -0.2t²i + 5tj + c' and i know at time t=0, 'r = 3i + 2j' but I'm not sure what to do to finish off the question. Thank you for any help! I know I have to substitute it in to find c, but I think I'm being a little silly and I'm not sure how to sub in and solve, when t is still in the first equation [/COLOR]:confused:
    So, at t=0

    r= 3i + 2j =-0.2x0²i + 5x0j + c = 0+c = c
    And so r= -0.2t²i + 5tj +3i + 2j

    And just group the i's and j's for good measure.
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    Okay so I'd end up with 'r = (3-0.2t²)i + (5t+2)j'

    I was wondering for part c, I assume I just sub in 10 to the equation for v, but how do I know the values of i and j at t=10?
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    (Original post by chris35)
    Okay so I'd end up with 'r = (3-0.2t²)i + (5t+2)j'

    I was wondering for part c, I assume I just sub in 10 to the equation for v, but how do I know the values of i and j at t=10?
    i,j are perpendicular unit vectors representing 1 m/s in the appropriate direction.

    This is true for all value of t.
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    Oh, so I just sub in t = 10 to get v = 1 m/s? Seems very easy!
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    (Original post by chris35)
    Oh, so I just sub in t = 10 to get v = 1 m/s? Seems very easy!
    Too easy.

    What have you done to get 1 m/s?

    Edit: Don't forget i and j represent vectors at right angles to each other, so you'd need to use Pythagoras to work out the magnitude of the combined velocities
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    Oh I assumed you meant i and j were just going to be 1, so I subbed 10 into 'v = (-0.4ti + 5j)' with i and j as 1, to get -4 + 5 = v, so v = 1. I'm guessing thats wrong though...
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    (Original post by chris35)
    Oh I assumed you meant i and j were just going to be 1, so I subbed 10 into 'v = (-0.4ti + 5j)' with i and j as 1, to get -4 + 5 = v, so v = 1. I'm guessing thats wrong though...
    They represent 1 m/s in the appropriate direction.

    Think of the -4i and the 5j as two sides of a right-angled triangle, and you need to find the length of the hypotenuse.
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    So I just need to find the hypotenuse?

    Edit: Sorry for this, I really appreciate the help!
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    (Original post by chris35)
    So I just need to find the hypotenuse?
    Yep. You need the length of the hypotenuse.
 
 
 
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