A scooter accelerates from rest for time $$t_1$$ at constant rate $$a_1$$ and then retards at constant rate $$a_2$$ for time $$t_2$$ and comes to rest. The correct value of $$\frac{t_1}{t_2}$$ will be:

The scooter starts from rest, accelerates at constant rate $$a_1$$ for time $$t_1$$, then decelerates at constant rate $$a_2$$ for time $$t_2$$ and comes to rest.

During the acceleration phase, the velocity increases from 0 to a maximum value $$v_{max}$$. Using $$v = u + at$$, we get $$v_{max} = 0 + a_1 t_1 = a_1 t_1$$.

During the deceleration phase, the velocity decreases from $$v_{max}$$ to 0. Using $$v = u - at$$, we get $$0 = v_{max} - a_2 t_2$$, which gives $$v_{max} = a_2 t_2$$.

Since both expressions equal $$v_{max}$$, we have $$a_1 t_1 = a_2 t_2$$. Therefore, $$\frac{t_1}{t_2} = \frac{a_2}{a_1}$$.