Velocity Vector

If a particle moves in space so that its position vector at time f is S = F(t), the vector derivative is called the velocity vector,

The length of the velocity vector is called the speed of the particle.

Theorems 1 and 2 show that:

• The velocity vector V is tangent to the curve.
• The speed |V| is equal to the rate of change of the length of the curve,

• The second derivative is called the acceleration vector

Example 4: Velocity, Speed, Acceleration Around the Unit Circle

Example 5: Velocity, Speed, Accelleration on a Parabolic Curve

Example 6: Position Vector