1. Motion during acceleration

The scooter starts from rest and accelerates with constant acceleration $a_1$ for time $t_1$.

Using $v = u + at$ we get $v = 0 + a_1 t_1 = a_1 t_1$

So, the velocity after the first phase is $v = a_1 t_1$

2. Motion during retardation

Now the scooter slows down with constant retardation $a_2$ for time $t_2$ and finally comes to rest.

Here initial velocity for this phase is $v = a_1 t_1$, final velocity is $0$, and acceleration is $-a_2$.

Again using $v = u + at$ $0 = a_1 t_1 - a_2 t_2$

Thus, $a_1 t_1 = a_2 t_2$

3. Find the ratio

$\frac{t_1}{t_2} = \frac{a_2}{a_1}$

4. Match with options

Option C is $\frac{a_2}{a_1}$ which matches our result.

Therefore, the correct answer is Option C.