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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.
x is position of particle’so unit of x is lengthpower of e should be dimensionless so unit of beta = 1/time(1-e^-beta*t) is dimension lessthen v’/beta = lengthso v’*time = lengththen v’ = length/timeso v’ = [M0L1T-1]beta = [M0L0T-1]Hope it clears.
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