Particle Motion Flashcard

Front

What does it mean when v(t)=0 for a particle?

Back

The particle is at rest.

Front

If velocity is negative and acceleration is positive, what happens to the speed?

Back

The speed is decreasing.

Front

What is the relationship between acceleration and velocity?

Back

The acceleration function is the first derivative of velocity.

Front

How do you determine intervals where an object's acceleration is negative?

Back

Analyze the sign of the acceleration function over the intervals.

Front

What is a critical value in a function?

Back

A critical value is where the derivative is zero or undefined, indicating potential local maxima or minima.

Front

What is the formula for acceleration in terms of position?

Back

Acceleration is the second derivative of position with respect to time.

Front

What does a positive acceleration indicate about a particle's motion?

Back

The particle's speed is increasing if the velocity is also positive.

Front

What does a negative acceleration indicate about a particle's motion?

Back

The particle's speed is decreasing if the velocity is also negative.

Front

How can you find the velocity function from the position function?

Back

Take the first derivative of the position function with respect to time.

Front

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

Back

It represents the acceleration of the particle.