Particle Motion (Calculus)

Front

What does it mean for a particle to be at rest?

Back

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

Front

How can you determine if a particle has negative velocity?

Back

A particle has negative velocity if its position graph is decreasing.

Front

What is the relationship between speed and velocity?

Back

Speed is the magnitude of velocity, represented as |v(t)|.

Front

How can you tell if a particle has positive velocity?

Back

A particle has positive velocity if its position graph is increasing.

Front

What indicates that a particle's speed is decreasing?

Back

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

Front

Define acceleration in the context of particle motion.

Back

Acceleration is the rate of change of velocity with respect to time, denoted as a(t).

Front

What is the significance of the derivative of position, x'(t)?

Back

The derivative of position, x'(t), represents the velocity of the particle.

Front

Explain the concept of instantaneous velocity.

Back

Instantaneous velocity is the velocity of a particle at a specific moment in time, calculated as the derivative of position.

Front

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

Back

Positive acceleration indicates that the particle's velocity is increasing.

Front

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

Back

Negative acceleration indicates that the particle's velocity is decreasing.