Understanding velocity as a vector quantity

Question

Why is velocity classified as a vector quantity. Can it be explained by the same way as force referring to the Phys.SE post Where am I confused about force addition?

score 2 · Answer 1 · answered Dec 28 '23 at 14:53

A simple answer is that velocity is a vector quantity because it has both magnitude and direction. A velocity of $1$ m/s eastwards is not the same as a velocity of $1$ m/s northwards, even though they have the same magnitude.

A more advanced answer is that velocity is a vector quantity because velocities can (and, indeed, must) be added together like vectors.

Note that speed - the magnitude of a velocity vector - is not a vector - it is a scalar quantity.

score 0 · Answer 2 · answered Dec 28 '23 at 17:02

A not so simple answer is that if the velocity has components $V_x, V_y, V_z$ in coordinate system $x, y, z$ and components $V_x', V_y', V_z'$ in coordinate system $x', y', z'$ then

velocity is a vector because

$$V^2_x+ V^2_y+ V^2_z=V^{'2}_x+ V^{'2}_y+ V^{'2}_z$$

score 0 · Answer 3 · answered Dec 28 '23 at 17:42

Velocity can be classified as a vector quantity because vectors have both a magnitude and a direction, whereas scalars only have a magnitude with no given direction.

Velocity has a magnitude and a direction so it is a vector. Speed only has a magnitude but no given direction, so it is a scalar.

score 0 · Answer 4 · answered Dec 28 '23 at 19:10

Take a football. Kick it towards your right. After that, kick it to your left with equal force. Then the ball has a rate of covering distance, say $2m/s$ in both cases. You'll notice that the ball moves in different directions in both cases.
How, then, do we specify which way the ball is going on paper? We need to add direction to the speed (which is the rate of covering distance) to fully describe its motion. We introduce a new quantity: velocity, which specifies the object's rate of covering distance (speed) as well as where it's going (direction). Which means, velocity is a vector quantity.
P.S. I assumed zero acceleration in all cases to simplify things. Actually, when you kick a football, you give it an acceleration, and velocity is acquired as a result of that.

Understanding velocity as a vector quantity

4 Answers4