Calc- Motion

Motion

What is velocity?

The derivative of position: v(t)=x′(t)

What is acceleration?

The derivative of velocity, or second derivative of position: a(t)=v′(t)=x′′(t)

When is the particle at rest?

When velocity equals zero: v(t)=0

When is the particle moving left

velocity is negative

When is the particle moving Right ;)

velocity is positive

When is the particle speeding up

velocity and acceleration have same sign

When is the particle slowing down?

velocity v(t) and acceleration a(t) have opposite signs

How do you find total distance traveled?

Use the integral of ∫ |v (t) | dt

How do you find net displacement?

Integrate velocity:

How do you find position at time t?

Use initial position and integrate velocity:

What is speed?

The absolute value of velocity: speed=∣v(t)∣

What is average velocity on [a,b]

Justification for particle slowing down

“The particle is slowing down because𝑣(𝑡) and 𝑎(𝑡) have opposite signs.”

Justification for particle speeding up

“The particle is speeding up because 𝑣(𝑡) and 𝑎(𝑡) have the same sign.”

Common mistake: forgetting to...

Use absolute value when calculating total distance!