Particle Motion for the AP Exam

Front

What is the position function of a particle traveling on a horizontal axis?

Back

The position function describes the location of a particle at any given time, often represented as x(t).

Front

How do you determine when a particle changes direction?

Back

A particle changes direction when its velocity changes sign, which can be found by setting the derivative of the position function to zero.

Front

What is the formula for average velocity on an interval [a, b]?

Back

Average velocity is calculated as \( \frac{x(b) - x(a)}{b - a} \).

Front

What does it mean if a particle's speed is decreasing?

Back

A particle's speed is decreasing if its velocity and acceleration have opposite signs.

Front

What is the relationship between velocity and acceleration?

Back

Velocity is the rate of change of position, while acceleration is the rate of change of velocity.

Front

How do you find the velocity from a position function?

Back

Velocity is found by taking the derivative of the position function, \( v(t) = x'(t) \).

Front

What does the notation |v(t)| represent?

Back

|v(t)| represents the speed of the particle, which is the magnitude of the velocity.

Front

What is the significance of the second derivative of the position function?

Back

The second derivative indicates the acceleration of the particle.

Front

How can you determine if a particle is speeding up?

Back

A particle is speeding up if its velocity and acceleration have the same sign.

Front

What is the position function given in the example: s(t) = t^3 + 3t^2 - 45t?

Back

This function describes the position of a particle over time.