The position of a point mass that moves in a straight line is given by $x(t) = At^2 + Bt + C$, where $t$ is time. Determine the units of $A$, $B$ and $C$.
The answer to the question is [A] = M/S^2, [B] = M/S and [C] = M but I don't know how to derive these answers; it seems like dimensional analysis is used but I'm not sure how one would go about doing it on this function.
Any help as to where these answers come from?
On
The left side (displacement $x$) has units of distance. Time $t$ has units of time.
All of the terms on the right must also have units of distance to be dimensionally correct (since they're added). You must add distances to distances. You cannot add distances to mass and have it make any sense.
So the first term $At^2$, dimensionally, is
$$[distance] = [A] [time]^2 \to [A] = \frac{[distance]}{[time]^2}.$$
Can you take it from here?
If the lhs has a dimension, all terms in the rhs must have the same dimension. So $$[M]= \frac {[M]}{[S]^2} [S]^2+ \frac {[M]}{[S]} [S]+ [M]$$
I hope and wish this makes things clearer to you.