Three motorcyclists P, Q and R, initially at the same point, start moving from rest on the same road in the same direction. They move with constant acceleration ` a_p,a_Q and a_R(a_Pgt a_Qgt a_R) ` . At any instant ,the separation between P and Q is ` (3)/(2) ` times the separation between Q and R . Then at any instant ` (2v_P+3v_R)/(v_Q) =` where `v_P,v_Qand v_R ` are instantaneous velocities of P, Q and R respectively.

Explanation

To solve the problem step by step, we will analyze the motion of the three motorcyclists P, Q, and R, who start from rest and move with different constant accelerations.

### Step 1: Define the Variables
Let:
- \( a_P \) = acceleration of motorcyclist P
- \( a_Q \) = acceleration of motorcyclist Q
- \( a_R \) = acceleration of motorcyclist R
- \( v_P \), \( v_Q \), \( v_R \) = instantaneous velocities of P, Q, and R respectively
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