Tully - Particle Motion Concepts (AP Calculus AB/BC)

When does a particle change direction?

A particle changes direction when velocity changes sign.

When velocity is negative, what direction is a particle moving?

A particle is moving to the left when velocity is negative.

When velocity is positive, what direction is a particle moving?

A particle is moving to the right when velocity is positive.

When is a particle moving to the left?

A particle moves to the left when v(t) is negative.

When is a particle moving to the right?

A particle moves to the right when v(t) is positive.

What does v(t) determine?

How fast the position of the particle is changing AND in what direction.

How is the total distance traveled by a particle calculated?

Integral of the absolute value of v(t) dt.

When is the speed of a particle decreasing?

Speed is decreasing when velocity and acceleration have opposite signs.

When velocity and acceleration have the opposite sign, what does that mean for the speed of a particle?

Speed is decreasing.

When is the speed of a particle increasing?

Speed is increasing when velocity and acceleration have the same sign.

When velocity and acceleration have the same sign, what does that mean for the speed of a particle?

Speed is increasing.

What equation(s) represent acceleration?

a(t) v'(t) x''(t)

What does a(t) determine?

a(t) determines how fast the velocity of a particle is changing.

What does a(t) represent?

acceleration

What does x(t) represent?

position of a particle

What does the phrase "initially" mean in particle motion?

t=0 time is zero

What does t represent in particle motion?

time

What equation(s) represent velocity?

v(t) x'(t) integral (a(t)) dt

When is a particle's velocity decreasing?

v(t) is decreasing when a(t) is negative.

When is a particle's velocity increasing?

v(t) is increasing when a(t) is positive.

What does the phrase "at rest" mean in particle motion

v(t)=0 velocity is zero

When the acceleration of a particle is negative, what does that mean for the particle's velocity?

velocity is decreasing when acceleration is negative

When the acceleration of a particle is positive, what does that mean for the particle's velocity?

velocity is increasing when acceleration is positive

What does v(t) represent?

velocity of a particle

What equation(s) represents position?

x(t) or s(t) integral (v(t)) dt Integral (integral (a(t)) dt) dt

What does the phrase "at the origin" mean in particle motion?

x(t)=0 position is zero

Particle motion generally happens along which straight line?

x-axis

How is the speed of a particle calculated?

|v(t)|

What does |v(t)| determine?

|v(t)| determines the speed of a particle