how do u kno if this is dimensionally correct?? HELP?

i am new to physics n i basically need all the help i can get so if its alright help me find the answer to this:

Show the expression x= vt + 1/2 at2 is dimensionally correct, where x is a coordinate and has units of length, v is velocity, a is acceleration and t is time.

thank you so SO MUCH

3 Answers

  • 9 years ago
    Favorite Answer

    Do you have any idea what unit/dimensional analysis is? It's the process of ensuring the units on the LHS (dependent) side of the equation match the units on the RHS (independent) side of it.

    So the LHS is x. What the heck is x? Is it volume? Is it speed? Is it time? No it's a length. It's not a "coordinate" a coordinate has at least two dimensions as in p(x,y). It is length, that's all it is.

    So LHS units are length units. Let's use the kms SI units. So x ~ meters.

    That means the RHS must equal meters. The units across the = sign must agree.

    Look at the first term. vt ~ m/s X s ~ m; so that's meters. Now the second term at^2 ~ m/s^2 X s^2 ~ m; and so is this. Both terms are meters; so the RHS is meters. That is consistent with the meters of x on the LHS.

    This is unit correct.

    I avoid using dimension in this context because these are metrics, units, not dimensions despite what some textbooks will tell you. [See source.]

    Source(s): Led the Metrics Group for the nation's second largest IT department.
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  • TBT
    Lv 7
    9 years ago

    x= vt + 1/2 at2

    [m] = [ m / s ] [ s] + 0.5 [ m/s^2] [ s^2]

    [m] = [m]

    the expression x= vt + 1/2 at2 is dimensionally correct ----proved

    Source(s): my brain (Prof TBT)
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  • 3 years ago

    definite it is. you could seem at any previous textbook to discover that out!! additionally no different capacity might desire to be dimensionally magnificent to illustrate: incorrect: E=mc3, mc4, mc5, .... good: E=mc2 Its the only one

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