Acceleration Vector
Definition
The acceleration vector represents the rate at which an object's velocity is changing over time. It includes both the magnitude (how fast the object is accelerating) and direction of acceleration.
Analogy
Imagine you are driving a car on a curvy road. The acceleration vector would be like your steering wheel, telling you how much and in which direction to turn to change your velocity.
Related terms
Velocity Vector: The velocity vector represents the rate at which an object's position is changing over time. It includes both the magnitude (speed) and direction of motion.
Displacement Vector: The displacement vector represents the change in position of an object from its initial point to its final point. It includes both magnitude (distance) and direction.
Force Vector: The force vector represents a push or pull acting on an object, causing it to accelerate. It includes both magnitude (strength) and direction of force.
"Acceleration Vector" appears in:
Practice Questions (5)
- If a particle’s velocity is given by the vector-valued function r(t) = ⟨2t, t^2⟩, what is its acceleration vector?
- A particle moves along a curve defined by the parametric equations x = 2cos(t) and y = 3sin(t). What is the magnitude of the acceleration vector of the particle at time t = π/6?
- A particle moves along a curve defined by the parametric equations x = t^3 and y = t^2. What is the acceleration vector of the particle at time t = 2?
- A particle moves along a curve defined by the vector-valued function r(t) = ⟨cos(t), sin(t), 2t⟩. What is the acceleration vector of the particle at time t = π/4?
- A particle in motion has a velocity vector given by v(t) = ⟨3t^2, 2t⟩. What is the acceleration vector of the particle?
Resources
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.