Particle Motion (Calculus)

Front

What indicates that a particle's speed is decreasing?

Back

When the particle's velocity and acceleration have different signs.

Front

Define velocity in the context of particle motion.

Back

Velocity is the speed of a particle in a specific direction.

Front

What is the relationship between the velocity function and position?

Back

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

Front

What does v(t) < 0 signify about a particle's motion?

Back

It means the particle is moving to the left.

Front

How is speed determined in particle motion?

Back

Speed is determined by the absolute value of velocity, |v(t)|.

Front

What is acceleration in terms of velocity?

Back

Acceleration is the rate of change of velocity with respect to time.

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 does a positive acceleration indicate about a particle moving to the left?

Back

It indicates that the particle is slowing down.

Front

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

Back

Average velocity is given by (s(b) - s(a)) / (b - a), where s(t) is the position function.

Front

What does the second derivative of position represent?

Back

The second derivative of position represents acceleration.