Particle Motion Unit 4 AP Calculus

Front

What condition indicates that a particle is at rest?

Back

The particle is at rest when its velocity, v(t), is equal to 0.

Front

How do you determine the total displacement from a position/time graph?

Back

Total displacement is the difference in position from the start to the end of the time interval.

Front

What is the relationship between acceleration and velocity in terms of derivatives?

Back

The acceleration function is the first derivative of the velocity function.

Front

Given the position function x = 3t² + 5t³ - 2t, how do you find the acceleration at a specific time?

Back

To find acceleration, take the second derivative of the position function and evaluate it at the given time.

Front

What is the formula for average velocity over a time interval?

Back

Average velocity is calculated as the change in position divided by the change in time.

Front

What does the first derivative of a position function represent?

Back

The first derivative of a position function represents the velocity of the particle.

Front

What does the second derivative of a position function represent?

Back

The second derivative of a position function represents the acceleration of the particle.

Front

How can you find the instantaneous velocity of a particle at a specific time?

Back

Instantaneous velocity can be found by evaluating the first derivative of the position function at that specific time.

Front

What is the significance of a zero velocity in particle motion?

Back

A zero velocity indicates that the particle is momentarily at rest.

Front

How do you interpret a position/time graph to find displacement?

Back

Displacement is the vertical distance between the initial and final positions on the graph.