Problem Solving Strategies Question

Near the end of class, Jillian's physics teacher writes a formula up on the board. Jillian quickly writes it down before leaving. Later that night while doing homework, she is unsure if she correctly copied the formula. What she wrote is:
`d = d_0 + v_0t + 1/2 at^2`
where `d, d_0` are distances measured in meters; `v_0` is velocity, measured in meters per second; `t` is time, measured in seconds; and `a` is acceleration, measured in meters per second squared.

She decides she will use dimensional analysis to determine if it is correct or not. She reasons that each term has to have the same units, and since the term on the left side of the equation and the first term on the right side of the equation are in meters, the other two terms need to be as well. The second term on the right side of the equation is

`"m"/"s" *"s"/1 = "m"`

and the last term is

`"m"/"s"^2 * "s"^2/1 = "m"`.

Since all terms are in meters, she decides that the equation she wrote down is right. Is she correct, and if not, what mistake did she make?

1. Yes, she is correct.
2. No. She assumed that all terms need to have the same units, when all terms need to be without units.
3. No. Although the variable `t` is squared, the units are not. Therefore, the units of the last term are m/s, which are different than the rest of the terms.
4. No. Jillian did the dimensional analysis incorrectly. The units of the second term on the right side come out to `"m"//"s"^2` and the units of the last term are `"m"//"s"^4`.