Constant Acceleration Average Velocity Calculator

What is Constant Acceleration Average Velocity?

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:

$$\overline{v}=\frac{v_0+v}{2}$$

Where:

• $\overline{v}$ 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:

$$\overline{v}=v_0+\frac{1}{2}at$$

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:

1. Identify the known values:
   • Initial velocity ($v_0$) = 5 m/s
   • Acceleration ($a$) = 2 m/s²
   • Time ($t$) = 10 s
2. Apply the average velocity formula: $$\overline{v}=v_0+\frac{1}{2}at$$
3. Substitute the known values: $$\overline{v}=5\text{ m/s}+\frac{1}{2}(2\text{ m/s²})(10\text{ s})$$
4. Perform the calculation: $$\overline{v}=5\text{ m/s}+10\text{ m/s}=15\text{ m/s}$$

Example and Visual Representation

Let's visualize the constant acceleration average velocity with our example:

This visual representation shows:

• The x-axis represents time, from 0 to 10 seconds
• The y-axis represents velocity, from 0 to 25 m/s
• The green line shows the linear increase in velocity over time
• The red dashed line represents the average velocity (15 m/s)
• The yellow point indicates the initial velocity (5 m/s) at t = 0 s
• The blue point indicates the final velocity (25 m/s) at t = 10 s