Saturday, November 19, 2011

How do you know when a vector is velocity?

Basically, how do you know when a given vector is velocity and WHY is velocity a vector? Velocity is basically just rate, right? Thats another thing, why are there the two equations: r=d\t and V=S\t arent they just saying the same thing except one deals with distance and one with displacement. Thanx to who can explain this! Please try to make it simple.|||Dude...use the correct slashes for division. "/" means division, and "\" doesn't really have any use in mathematics.








The deal is, velocity is a vector BY DEFINITION. Yes it is a rate, but it is a rate of a vector quantity. Namely position. You need BOTH distance from origin and direction to specify position, hence it is a vector.





Change in position (aka displacement) per unit time yields a vector quantity.


UNLIKE change in distance per unit time, which yields a scalar, which we call speed.


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"how do you know when a given vector is velocity?"





Check the units. Velocity has units of meters/second.





Other vectors have different units. Such as acceleration has units of meters/second^2. OR displacement has units of meters. Or force has units of Newtons.|||Identifying a velocity vector should be easy. Just see the units, should be m/s. Even if someone gives you a vector, units must be specified, otherwise it makes no sense.


Take two cars. One moving west, other north. Same speed. Are they same? I think not, directions are different right? Just to take this into consideration, velocity was created. Any quantity which changes with change in direction is similar to velocity and this group is given a name, vector.


V=S/t gives average velocity in the direction of displacement only.


r=d/t Distance is scalar as you might know. So r cannot be velocity, has to be average speed, so that LHS=RHS=scalar quantities|||When a rate is vector it is a velocity. A rate is one dimensional velocity. In one dimensional situations the terms are often used interchangeably.





If I am going 50 mph in my car this is a rate. If I am going South at 50 mph in my car, this is a velocity. Velocity has both a magnitude and a direction.|||Velocity,V and Speed,R both have same magnitude but they aren't same things.Velocity has direction + Magnitude ,so it is a vector.Speed has only magnitude,thus it is scalar.Velocity is not just rate,it is rate + direction that's why it is a Vector.I hope it would help you.:-)

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