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    Hey all, I'm stuck on the following question:

    "A particle has an initial velocity of i + 2j and is accelerating in the direction i + j. If the magnitude of the acceleration is 5 root 2, find the velocity vector and the speed of the particle after 2 seconds."

    I don't even know where to start, could someone please give me some tips on how to go about this question? Thanks!
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    i think this means it has an acceleration of 5root 2 in direction of the hypotenuse of a triangle with 1 1 root2 as sides therefore 2x^2 =50 therefore its acceleration with magnitude 5 in each direction therefore after 2 seconds it will have increased by 10 m/s add that onto original values. i dont know if this is the case we didnt have vectors in our mechanics because ocr is crap
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    (Original post by Skycat)
    Hey all, I'm stuck on the following question:

    "A particle has an initial velocity of i + 2j and is accelerating in the direction i + j. If the magnitude of the acceleration is 5 root 2, find the velocity vector and the speed of the particle after 2 seconds."

    I don't even know where to start, could someone please give me some tips on how to go about this question? Thanks!
    IF you'd been told the acceleration was i +j, THEN you'd know it's magnitude was \sqrt{2}, by using pythagoras (draw a diagram if you're uncertain).

    BUT you're told the DIRECTION vector for the aceleration is i+j, so you need to scale that direction vector so that it has the correct magnitude to represent the acceleration.

    Since the magnitude of the acceleration is 5\sqrt{2} and the magnitude of the direction vector is \sqrt{2} then it's been scaled by a factor of 5.

    So the acceleration vector is 5 times the direction vector, i.e. 5(i+j), or 5i + 5j

    Hope that helps and that you can take it from there.
 
 
 
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