A particle starts from rest and moves under constant acceleration in a straight line. Find the ratio of displacement (a) in successive second and (b) in successive time interval `t_(0)`.

Explanation

To solve the problem, we will break it down into two parts: (a) finding the ratio of displacement in successive seconds, and (b) finding the ratio of displacement in successive time intervals `t_(0)`.

### Part (a): Ratio of Displacement in Successive Seconds

1. **Understanding the motion**: The particle starts from rest and moves under constant acceleration. The initial velocity \( u = 0 \) and the acceleration is \( a \).

2. **Displacement in the first second**:
The displacement \( s_1 \) during the first second can be calculated using the formula:
...