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dimensional analysis

the displacement of an object of mass m after time t when a net force F acts on it is dependent on F, t and m. use dimensional analysis to work out the formula for the displacement of the object.

Here's how I'd think of it:The three variables F, t and m have dimensions MLT^-2, T and M respectively.Now you have to consider how these three require to be combined to produce a quantity of dimension 'L'  i.e. a displacement.  You have to multiply the dimensions of F by M^-1 and by T^2 to do that.Without actually spelling out the answer, I hope that's enough to point you the right way.
Tom G.
07 September 2016
Hello, did you find an answer to your question?
Sujata S.
15 September 2016
Tom G is the only person who understands what dimensional analysis means.We have three basic dimensions: M = mass, L = length and T = timeWe know force = mass × accelerationThe dimensions of mass is MThe dimensions of acceleration is LT⁻² (compare to its unit meters/second²)So the dimensions of force are M × LT⁻² or just MLT⁻²We need to find displacement (length) which is L = _________ .Using force = MLT⁻², time = T and mass = M we need to cancel the M and T⁻² of force to be left with the dimensions of displacement (L):L = MLT⁻² × T²/M   i.e.   displacement = force × time²/mass
Sam P.
23 September 2016
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