A particle, starting from rest, moves in a straight line with constant acceleration `a_0 ` for a time interval `t_0`.Then is accelerates at a constant rate `2a_0` for time interval ` 2t_0` .The distance travelled by the particle in time ` 3t_0` from the starts is S . Then ` (S)/(a_0t_0^(2) )= `

Explanation

To solve the problem step by step, we will analyze the motion of the particle during the two phases of its movement.

### Step 1: Calculate the distance traveled in the first phase (0 to t₀)
The particle starts from rest and moves with a constant acceleration \( a_0 \) for a time interval \( t_0 \).

Using the equation of motion:
\[
s_1 = ut + \frac{1}{2} a t^2
...