Problem 5: (a) Suppose that the displacement of an object is related to time according to the expression x=Bt2. What are the dimensions of B?
(b) A displacement is related to time as x = Asin(2πft), where A and f are constants. Find the dimensions of A?
(a) Given data: x = displacement
t = time
Required: Dimensions of B in x = Bt2
(b) Given data: x= displacement
Angle = 2πft
Required : Dimensions of A in x = Asin(2πft)
Now sin(2πft) is the ratio between two similar quantities, i-e, lengths (length of perpendicular/ length of hypotenuse), therefore, it has no dimensions.