Constant acceleration average velocity is a concept in physics that describes the average speed of an object moving with constant acceleration over a given time interval. It is particularly useful in analyzing motion where the velocity changes at a constant rate, such as in free fall or uniformly accelerated motion.
Formula
The formula for average velocity under constant acceleration is:
\[ \bar{v} = \frac{v_0 + v}{2} \]
Where:
\(\bar{v}\) is the average velocity
\(v_0\) is the initial velocity
\(v\) is the final velocity
This formula can also be expressed in terms of initial velocity, acceleration, and time:
\[ \bar{v} = v_0 + \frac{1}{2}at \]
Where:
\(a\) is the acceleration
\(t\) is the time interval
Calculation Steps
Let's calculate the average velocity of an object that starts with an initial velocity of 5 m/s and accelerates at 2 m/s² for 10 seconds:
Identify the known values:
Initial velocity (\(v_0\)) = 5 m/s
Acceleration (\(a\)) = 2 m/s²
Time (\(t\)) = 10 s
Apply the average velocity formula:
\[ \bar{v} = v_0 + \frac{1}{2}at \]
Substitute the known values:
\[ \bar{v} = 5 \text{ m/s} + \frac{1}{2}(2 \text{ m/s²})(10 \text{ s}) \]