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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

Given that


(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.



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