Guest Posted March 22, 2015 Report Share Posted March 22, 2015 Why the magnitude of a velocity vector is speed? Cant it be distance? Reply Link to post Share on other sites More sharing options...
Slovakov Posted March 22, 2015 Report Share Posted March 22, 2015 The magnitude of a vector (or length of a vector in other words) gives a magnitude of the same phenomenon but with no regards to direction. So the magnitude of velocity vector is velocity with no given direction, and the magnitude of distance vector is distance with no direction given. Even looking at units, vector megnitude of velocity would be: sqrt( (m/s)2 + (m/s)2 + (m/s)2) which still results as m/s, meaning.... speed! Velocity and distance are linked but in a different way... or could I say, differential. Velocity is a derivative of distance covered in time, so we cannot deduce distance from the vector of velocity if no time scope is given. 3 Reply Link to post Share on other sites More sharing options...
Vioh Posted March 22, 2015 Report Share Posted March 22, 2015 Why the magnitude of a velocity vector is speed? Cant it be distance? It all depends on the definitions of these words in everyday language. It can’t be called distance, because that’s not how people generally understand the word. In physics/mathematics, the rules & definitions are quite simple: Displacement () is magnitude plus direction, defined as the change in positions; mathematically Distance () is only the magnitude, defined as the absolute value displacement; mathematically Velocity () is magnitude plus direction, defined as change in displacement divided by change in time; mathematically Speed is only the magnitude, defined as change in distance divided by change in time; mathematically (where & are position vectors of point A & B, and the arrow is the vector notation. In short, it is better to define velocity based upon the concept of displacement; similarly it’s better to define speed using the concept of distance. That way, it’ll become much more intuitive to see. 2 Reply Link to post Share on other sites More sharing options...
mechnight Posted March 22, 2015 Report Share Posted March 22, 2015 Velocity and distance are linked but in a different way... or could I say, differential. Velocity is a derivative of distance covered in time, so we cannot deduce distance from the vector of velocity if no time scope is given. Love the pun. Reply Link to post Share on other sites More sharing options...
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