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 motorcyclists P, Q, and R using the information given about their accelerations and the relationship between their separations.

### Step 1: Write the equations for the distances traveled by each motorcyclist.
Since all three motorcyclists start from rest and move with constant acceleration, we can use the equation of motion:
\[ S = \frac{1}{2} a t^2 \]
where \( S \) is the distance traveled, \( a \) is the acceleration, and \( t \) is the time.

For motorcyclist P:
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