A particle starts moving in a straight from rest with constant acceleration until it reaches velocity v. The distance travelled by it until this point is x . Then, it covers a further distance x at constant velocity. Finally, it slows down to rest at a constant rate such that it covers distance 2x. The total time for which the particle moved is T .Then ` ,(Tv)/(x)= `

Explanation

To solve the problem step by step, we will analyze the motion of the particle in three distinct phases: acceleration, constant velocity, and deceleration.

### Step 1: Analyze the first phase (Acceleration)
The particle starts from rest and accelerates to a velocity \( v \) over a distance \( x \).

Using the first equation of motion:
\[
v = u + at
...