Constant velocity means that the object in motion is moving in a straight line at a constant speed.

This line can be represented algebraically as ,\( x=x_{0}+v t \) where x₀ represents the position of the object at t=0, and the slope of the line indicates the object’s speed.

The velocity can be positive or negative and is indicated by the sign of our slope. This tells us in which direction the object moves.

Newton’s second law ( \( F=m a \)) suggests that when a force is applied to an object, the object will experience acceleration.

If the acceleration is 0, the object shouldn’t have any external forces applied to it. Mathematically, this can be shown as the following:

\( A=\frac{d v}{d t}=0 \Rightarrow v= \) const

If an object is moving at constant velocity, the graph of distance vs. time (x vs. t) shows the same change in position over each interval of time.

Therefore the motion of an object at constant velocity is represented by a straight line: , where x₀ is the displacement when t=0 (or at the y-axis intercept)