**Problem Statement:**
A particle is projected from the ground with an initial speed u at an angle θ with the horizontal. We need to find the average velocity of the particle between its point of projection and the highest point of the trajectory.

**Solution:**
To find the average velocity of the particle between its point of projection and the highest point of the trajectory, we need to calculate the displacement of the particle and the time taken to reach the highest point.

Let's break down the problem into steps:

1. Initial Velocity Components:
- The initial velocity of the particle can be resolved into horizontal and vertical components.
- The horizontal component (u_x) remains constant throughout the motion and is given by u_x = u * cos(θ).
- The vertical component (u_y) changes as the particle moves in a projectile motion and is given by u_y = u * sin(θ).

2. Time of Flight:
- The time taken by the particle to reach the highest point is half of the total time of flight.
- The time of flight (T) can be calculated using the vertical component of velocity and acceleration due to gravity.
- The equation for time of flight is T = 2 * (u_y / g), where g is the acceleration due to gravity.

3. Displacement:
- The displacement of the particle can be calculated using the vertical component of velocity, time of flight, and acceleration due to gravity.
- The equation for displacement (S) is S = u_y * T - 0.5 * g * T^2.

4. Average Velocity:
- The average velocity (V_avg) is calculated by dividing the displacement by the time taken to reach the highest point.
- The equation for average velocity is V_avg = S / (T / 2).

By substituting the values of displacement and time of flight calculated in steps 3 and 2 respectively, we can find the average velocity.

Note: Make sure to use appropriate units and convert angles to radians if necessary.

This is the detailed solution to finding the average velocity of the particle between its point of projection and the highest point of the trajectory.