Question

(a) suppose that the displacement of an object is related to time according to the expression x = bt2. what are the dimensions of b?

Answer 1

Displacement x would be in terms of length, while t would be in terms of time.
Therefore the equation would have units of:
length = (b)*time^2
b = length/(time^2)
Therefore, the units of the constant b should be in length per time^2 (for example, in m/s^2, such as in acceleration).