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Uniform linear motion

Uniform linear motion is most basic in all motions. The uniform linear motion is a motion that does not change the velocity and moving direction of the object. For example, if an object is moving in uniform linear motion at 100 km per hour to the west. An hour later, the object will find in 100 km to the west of the original position. This word "uniform linear motion" is important to define the motion of object. Even if the object in 100 km west after an hour, it is unclear what velocity the object took to reach that place without the word "uniform linear motion." Assume an object A which move in uniform linear motion at 100 km per hour westward and the object B which stops for 30 minutes at first and then move westward at 200 km per hour. An hour later, both objects A and B are located in 100 km to west. However, object A always moved at 100 km per hour, but the object B moved at 0 km per hour and 200 km per hour. In other words, an object which moves in uniform linear motion does not change the velocity and moving direction at all times.

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Figure 1 The object perform uniform linear motion at speed of \( v \)

As shown in figure 1, we consider an object that is moving in uniform linear motion at a velocity of \( v \) in the right direction. The object speed is always \( v \), so the object will never accelerate. According to Newton's first law of motion, an object which moves in uniform linear motion keeps its state unless an external force will be applied. In short, we obtain the following equation; \begin{equation} a = \frac{dv}{dt} = \frac{d^2x}{dt^2} = 0 \end{equation} where \( a \) is acceleration. Here, acceleration is the amount that velocity changes per unit time, so you differentiate velocity to get acceleration. And the velocity is the amount that position changes per unit time, so you differentiate position to get velocity. In other words, the second derivative of the position is acceleration. By substitute \( a= 0 \) to the equation of motion, \begin{equation} F = 0 \end{equation}\ The fact an object that moves in uniform linear motion is not applied any forces and acceleration seems to be simple, but it's imperative. Here, \( F= 0 \) does not mean that completely no force applied to the object. Precisely, this means that "an object is not applied force or the applied forces are balanced, so the resultant force applied to the object is zero." Therefore, an object moves in uniform linear motion continues to move in the same velocity if the object is applied forces that cancel out each other.

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