To find the average velocity of a body with constant acceleration from any two points in its motion, you can use the following formula:
Average velocity = (Final velocity - Initial velocity) / Time interval
Let's denote the initial velocity as "v0", the final velocity as "v", and the time interval as "t". If the body has constant acceleration, you can relate the final velocity to the initial velocity and time using the equation of motion:
v = v0 + a * t
where "a" represents the constant acceleration.
Now, we can substitute this equation into the formula for average velocity:
Average velocity = (v - v0) / t
Since "a" is constant, we can further manipulate the equation of motion to express the final velocity in terms of the initial velocity, acceleration, and time:
v = v0 + a * t
By substituting this expression into the formula for average velocity, we get:
Average velocity = ((v0 + a * t) - v0) / t
Simplifying further, we have:
Average velocity = a * t / t
The time interval cancels out, leaving us with:
Average velocity = a
Therefore, the average velocity of a body with constant acceleration is equal to the acceleration itself. This result holds regardless of the specific values of the initial and final velocities or the time interval considered.