Velocity Vector
Definition
A velocity vector represents both the speed and direction of an object's motion. It is a mathematical representation that combines magnitude (speed) and direction into a single quantity.
Analogy
Imagine you are playing a video game where you control a spaceship. The velocity vector would be like an arrow on your screen, showing the speed and direction in which your spaceship is moving.
Related terms
Displacement Vector: Similar to velocity vectors, displacement vectors represent the change in position of an object. They also include magnitude (distance) and direction.
Acceleration Vector: An acceleration vector shows how an object's velocity changes over time. It includes both magnitude (rate of change of speed) and direction.
Scalar Quantity: Unlike vectors, scalar quantities only have magnitude but no specific direction. Examples include distance, speed, temperature, or mass.
"Velocity Vector" appears in:
Subjects (2)
Practice Questions (4)
- If a particle’s position vector is r(t) = ⟨cos(t), sin(t)⟩, what is its velocity vector?
- A particle moves along a curve in the plane with a velocity vector given by v(t) = ⟨2t, 4t^3⟩. If the particle’s initial position is ⟨1, 4⟩, what is the position vector of the particle at time t = 2?
- Consider a particle moving along a curve in the plane defined by the parametric equations x = 2t and y = t^2. What is the velocity vector of the particle at t = 3?
- A particle in motion has a velocity vector given by v(t) = ⟨3t^2, 2t⟩. What is the acceleration vector of the particle?
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