How do you find the position of a particle at time t given its velocity vector and initial position?

Integrate the velocity vector to find the position vector. 2. Use the initial position to solve for the constant of integration. 3. Plug in t to find the position at that time.

Flip to see [answer/question]

Revise later

SpaceTo flip

If confident

All Flashcards

How do you find the position of a particle at time t given its velocity vector and initial position?

Integrate the velocity vector to find the position vector. 2. Use the initial position to solve for the constant of integration. 3. Plug in t to find the position at that time.

How do you find the distance of a particle from the origin at time t, given its velocity vector and initial position?

Integrate the velocity vector to find the position vector. 2. Use the initial position to solve for the constant of integration. 3. Plug in t to find the position at that time. 4. Use the distance formula to find the distance from the origin.

What is a vector-valued function?

A function whose domain is a set of real numbers and whose range is a set of vectors.

What does integrating a vector-valued function give?

The antiderivative of the vector-valued function, which can represent position given a velocity function.

What is the form of a 2D vector-valued function?

Can be written as $r(t) = f(t)i + g(t)j$ or $r(t) = \langle f(t), g(t) \rangle$ .

How are the components of a vector-valued function integrated?

Each component is integrated separately, treating each as its own integral problem.

What do the constants of integration represent when integrating a vector-valued function representing velocity?

The initial position of the particle.

What information can be obtained by integrating a vector-valued acceleration function?

The velocity function, plus a constant of integration representing initial velocity.

All Flashcards

How do you find the position of a particle at time t given its velocity vector and initial position?

Integrate the velocity vector to find the position vector. 2. Use the initial position to solve for the constant of integration. 3. Plug in t to find the position at that time.

How do you find the distance of a particle from the origin at time t, given its velocity vector and initial position?

Integrate the velocity vector to find the position vector. 2. Use the initial position to solve for the constant of integration. 3. Plug in t to find the position at that time. 4. Use the distance formula to find the distance from the origin.

What is a vector-valued function?

A function whose domain is a set of real numbers and whose range is a set of vectors.

What does integrating a vector-valued function give?

The antiderivative of the vector-valued function, which can represent position given a velocity function.

What is the form of a 2D vector-valued function?

Can be written as $r(t) = f(t)i + g(t)j$ or $r(t) = \langle f(t), g(t) \rangle$ .

How are the components of a vector-valued function integrated?

Each component is integrated separately, treating each as its own integral problem.

What do the constants of integration represent when integrating a vector-valued function representing velocity?

The initial position of the particle.

What information can be obtained by integrating a vector-valued acceleration function?

The velocity function, plus a constant of integration representing initial velocity.