Position function
Definition
The position function describes the location of an object in relation to a reference point or origin. It shows how an object's position changes over time.
Analogy
Imagine playing a video game where your character moves around on a map. The position function would be like coordinates on that map, telling you exactly where your character is located at any given moment.
Related terms
Displacement: The change in position of an object from its initial position to its final position.
Distance traveled: The total length covered by an object during its motion, regardless of direction.
Initial condition(s): Specific values or conditions given for variables in a mathematical equation or problem.
"Position function" appears in:
Study guides (2)
Practice Questions (12)
A woman is biking to work; her position function is given by s(t) = 3t^3 - 4t^2 + 2. What is her velocity at time t = 2?
A particle moves along a straight line, and its position function is given by x(t) = sin(t). At which of the following times is the particle momentarily at rest?
Consider a particle moving along a path. The position function of the particle is given by s(t) = t^3 - 2t^2 + 4t - 3. What is the velocity function of the particle?
Consider a particle moving along a path. The velocity function of the particle is given by v(t) = 4t - 3. What is the position function of the particle?
Consider a particle moving along a path. The position function of the particle is given by s(t) = 2t^3 - 3t^2 + 4t + 1. What is the acceleration function of the particle?
Consider a particle moving along a path. The velocity function of the particle is given by v(t) = 3t^2 + 2t - 5. What is the position function of the particle?
How do we find the position function of an object if given its acceleration function?
Consider a particle moving along a path. The velocity function of the particle is v(t) = 3e^t - 2t. What is the position function of the particle?
If the position function of a ball is s(t) = 7t^2 + 3, what is the velocity of the ball at t = 4?
How can we find the position function of an object given its velocity function?
If the position function of a car is given by s(t) = 3t^3 - 2t^2 + 5t, what is the velocity of the car at t = 2?
If the position function of a particle is given by s(t) = 5sin(t) + 2cos(t), what is the velocity of the particle at t = π/4?
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