**Problem 5:** (a) Suppose that the displacement of an object is related to time according to the expression x=Bt^{2}. 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?

**Solution**

**(a)** Given data: x = displacement

t = time

Required: Dimensions of B in x = Bt^{2}

Given that

Therefore,

(b) Given data: x= displacement

Angle = 2πft

Required : Dimensions of A in x = Asin(2πft)

Since

Therefore,

Now sin(2πft) is the ratio between two similar quantities, i-e, lengths (length of perpendicular/ length of hypotenuse), therefore, it has no dimensions.

Hence

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