# Find velocity with vector or without vector

• Istiak
In summary, the conversation discusses the equation ##\frac{1}{2}mv_2^2=\frac{1}{2}m(-\dot{y}+\dot{x})^2## and the relationship between vector ##v_2## and simple velocity in the ##x## and ##y## coordinate system. It is also mentioned that the Pythagorean theorem only applies to right-triangles and that Lagrange's Equations are considered advanced physics.
Istiak
Homework Statement
Find velocity with vector or without vector
Relevant Equations
vector

At the moment he wrote that ##\frac{1}{2}mv_2^2=\frac{1}{2}m(-\dot{y}+\dot{x})^2##

But, I know from vector ##v_2=\sqrt{(-\dot{y})^2+(\dot{x})^2}##. At first I (he) found that ##v_2=-\dot{y}+\dot{x}##. But, when thinking of simple velocity in ##x## and ##y## coordinate then I get $$v^2=\dot{x}^2+\dot{y}^2$$ (I remember the equation from my last book). What am I taking wrong with the top (absolute top) equation?

In the equation, ##v_2=\sqrt{(-\dot{y})^2+(\dot{x})^2}## if I square both side than I get the equation which I gave above. So, can we write that ##v=\dot{x}+\dot{y}##. Then, if we square both side than that's simple algebraic expression. Maybe, this time I am mixing Algebra with Vector this time.

The Pythagorean theorem applies only to right-triangles.
In this problem, ##x## and ##y## are not the legs of a right-triangle in space,
and neither are ##\dot x## and ##\dot y##.

The labels of the configuration coordinates are arbitrary.
Instead of the pair ##x## and ##y## (which is suggesting unrelated ideas),
use another pair (like ## c## and ## d##).By the way, I don't think Lagrange's Equations are considered "introductory physics" in this forum.

Istiak
robphy said:
By the way, I don't think Lagrange's Equations are considered "introductory physics" in this forum.

Istiakshovon said:
Yeah, for me at least, problems involving the Lagrangian qualify for the Advanced Physics schoolwork forum.

## 1. What is velocity and how is it different from speed?

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the magnitude (speed) and direction of motion. Speed, on the other hand, is a scalar quantity that only describes the rate of change of an object's position without considering direction.

## 2. How do you calculate velocity with a vector?

To calculate velocity with a vector, you need to know the displacement (change in position) of an object and the time it took for that displacement to occur. The velocity vector is then calculated by dividing the displacement vector by the time interval.

## 3. Can velocity be negative?

Yes, velocity can be negative. A negative velocity indicates that the object is moving in the opposite direction of the chosen positive direction. For example, if the positive direction is to the right, a negative velocity would mean the object is moving to the left.

## 4. Is it possible to find velocity without a vector?

Yes, it is possible to find velocity without a vector. This can be done by using the formula velocity = distance/time, where distance is the total distance traveled by an object and time is the total time it took for that distance to be covered. However, this will only give you the speed and not the direction of motion.

## 5. How can velocity be represented graphically?

Velocity can be represented graphically by a vector arrow. The length of the arrow represents the magnitude (speed) of the velocity, while the direction of the arrow represents the direction of motion. The arrow is drawn from the starting point to the ending point of the object's motion.

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