A particle starts from rest with a constant acceleration. At a time t second, the speed is found to be 100 m/s and one second later the speed becomes 150 m/s. Find a. the acceleration and b. the distance travelled during the `(t+1)^(th)` second.

Explanation

To solve the problem step by step, we will first find the acceleration of the particle and then calculate the distance traveled during the \( (t+1)^{th} \) second.

### Step 1: Find the acceleration

Given:
- Initial speed at time \( t \) seconds, \( u = 100 \, \text{m/s} \)
- Speed at \( t + 1 \) seconds, \( v = 150 \, \text{m/s} \)
- Time interval, \( \Delta t = 1 \, \text{s} \)
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