Particle Motion Unit 4 AP Calculus

Front

What is the formula for the position of a particle in motion?

Back

The position of a particle can be represented by a function x(t), where t is time.

Front

How do you find the instantaneous velocity of a particle?

Back

The instantaneous velocity is found by taking the derivative of the position function x(t) with respect to time t.

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 zero.

Front

What is the relationship between speed and velocity?

Back

Speed is the magnitude of velocity and does not include direction, while velocity includes both speed and direction.

Front

How can you determine when a particle is speeding up?

Back

A particle is speeding up when its velocity and acceleration have the same sign (both positive or both negative).

Front

What is average velocity?

Back

Average velocity is defined as the change in position divided by the time interval over which the change occurs.

Front

How do you calculate average velocity from a position function s(t)?

Back

Average velocity from s(t) over the interval [a, b] is given by (s(b) - s(a)) / (b - a).

Front

What is the significance of the derivative in particle motion?

Back

The derivative of the position function gives the velocity function, which describes how the position changes over time.

Front

What does a velocity graph indicate about a particle's motion?

Back

A velocity graph shows the speed and direction of a particle's motion, indicating when it is speeding up, slowing down, or at rest.

Front

What is the second derivative of the position function?

Back

The second derivative of the position function is the acceleration function, which describes how the velocity changes over time.