Formula: $s_n$ = u + $\frac{a}{2}$(2n - 1)

Key points:

1. $s_n$ is displacement in the nth second, NOT distance
2. $s_n$ can be negative (means body moved backward in that second)
3. When $s_n$ = 0, the body has zero displacement in that second (momentary reversal)
4. $s_n$ = 0 when n = $\frac{1}{2}$ - u/a + 1/2 = $\frac{1 - 2u/a + 1}{2}$... Better: set u + a$\frac{2n-1}{2}$ = 0

Finding when body reverses: Body reverses when v = 0. $t_{reverse}$ = -u/a (must be positive, so u and a must have opposite signs)

Distance calculation: Split motion at the reversal point.

• Distance from t=0 to $t_{reverse}$: |$s_1$|
• Distance from $t_{reverse}$ to $t_{total}$: |$s_2$|
• Total distance = |$s_1$| + |$s_2$|