Velocity/Acceleration Magnitude & Direction: Explained

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When asking for the magnitude and direction of velocity or acceleration, a person seeks to understand both how fast an object is moving and the specific direction of that movement. The magnitude of velocity, often referred to as speed, quantifies the rate of motion without indicating direction. In contrast, velocity encompasses both speed and directional information, providing a complete picture of an object's movement. Similarly, acceleration includes both the rate of change of velocity and its direction. Understanding these concepts is essential for analyzing motion in physics.
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What is a person looking for if they ask for the magnitude and the direction of velocity or acceleration, or anything for that matter?
 
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The magnitude of the velocity is sometimes called speed and simply indicates how fast something is moving. The velocity itself includes both the magnitude and direction - i.e. which way it's going. Likewise with acceleration.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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