Introduction:
In this scenario, two particles A and B start from rest. Particle A has a constant acceleration (a) towards the East, while particle B increases its speed at a constant rate (b) towards particle A. The objective is to determine the time at which particle B meets particle A and calculate the total distance traveled by particle B. It is given that b is greater than a.

Approach:
To solve this problem, we can analyze the motion of both particles and find the point of intersection. We'll start by understanding the motion of particle A and then determine the motion of particle B in relation to A.

Motion of Particle A:
Since particle A has a constant acceleration (a) towards the East, its velocity will continuously increase in that direction. Assuming the initial position of particle A as the origin, we can use the equations of motion to describe its motion.

Let's consider the time taken by particle A to reach the point of intersection as (t) and the distance traveled by A in this time as (x).

The equation of motion for particle A can be expressed as:
x = ut + (1/2)at^2
Since the initial velocity (u) of particle A is zero, the equation simplifies to:
x = (1/2)at^2

Motion of Particle B:
Particle B increases its speed at a constant rate (b) towards particle A. However, the direction of velocity is always towards A. This implies that particle B is constantly accelerating towards particle A.

In order to determine the motion of particle B, we need to consider its velocity in terms of the relative velocity between A and B. Let's assume the relative velocity of B with respect to A as (v).

Since the velocity of B is always directed towards A, the relative velocity (v) can be expressed as:
v = -b

Now, let's consider the time taken by particle B to meet particle A as (t') and the distance traveled by B in this time as (y).

The equation of motion for particle B can be expressed as:
y = vt' + (1/2)bt'^2
Replacing the value of relative velocity (v) as -b, we get:
y = -bt' + (1/2)bt'^2

Calculation:
Since particle A and particle B meet at the point of intersection, their distances (x and y) are equal. Therefore, we can equate the equations for particle A and particle B to find the time of intersection (t').

(1/2)at^2 = -bt' + (1/2)bt'^2
Simplifying the equation, we get:
(at^2) - (bt') = (1/2)bt'^2
Rearranging the terms, we have:
(at^2) - (1/2)bt'^2 = bt'
Factoring out (t') from the equation, we get:
t'(a - (1/2)bt') = at^2
Dividing both sides by (a - (1/2)bt'), we get:
t' = (at^2) / (a - (1/2)bt')

Total Distance Traveled by B:
To calculate the total distance traveled by particle B, we need to