Q.The position of particle in a specific rectilinear motion is given by x(t)=v’/beta(1-e^-beta*t) where beta and v’ are constants. Determine the dimensions of v’*beta. While solving it , How to know x(t) gives some distance or v’ is speed.Is there a way to deduce equations and get their meaning,i.e.physical quantity.

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Khimraj · Answer

x is position of particle’so unit of x is length power of e should be dimensionless so unit of beta = 1/time (1-e^-beta*t) is dimension less then v’/beta = length so v’*time = length then v’ = length/time so v’ = [M 0 L 1 T -1 ] beta = [M 0 L 0 T -1 ] Hope it clears.

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