How Does Dimensional Analysis Validate Units in Physics Problems?

[JakePearson]

given a distance s = 8.6m, time t = 2s, and a mass = 1.01kg, evaulate the expression to a physically appropriate accuracy?

m³ = 1.01³ = 3.03kg

is this correct

 

[fluidistic]

No.
I don't know if I understand what they ask. Do they ask for $$m^3$$, where m is the mass? If so, check out the units that you got. They are wrong. $$(1.01 kg)^3=$$?
I don't see the point of s=8.6 and t=2s though.

 

[tomcue]

?

No, this is not correct. Dimensional analysis involves using the units of measurement to evaluate an expression, not just the numerical values. In this case, the units for distance (m), time (s), and mass (kg) cannot be combined to equal the unit for m3. Therefore, the expression cannot be evaluated. A physically appropriate accuracy would be to use the given values as they are, without trying to convert them into a different unit.