Particle Motion (conceptual)

A particle moves to the right, when...

• velocity is positive

• velocity is negative

• acceleration is positive

• acceleration is negative

How do I determine if a particle is switching directions?

• Find where acceleration is 0

• Find where acceleration switches signs

• Find where velocity is 0

• Find where velocity switches signs.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

To calculate the total distance traveled from a to b, use the following:

•  $\int_a^bv\left(t\right)dt$  

•  $\int_a^b\left|v\left(t\right)\right|dt$  

•  $x\left(a\right)+\int_a^bv\left(t\right)dt$  

•  $v\left(b\right)-v\left(a\right)$  

To determine if a particle is speeding up,

• Determine if velocity is positive

• Determine if acceleration is positive

• Determine if acceleration and velocity are the same sign

• Determine if acceleration and velocity are opposite signs

To calculate the final position (x(b)) of a particle, given that initial position x(a) is known, use which of the following?

•  $\int_a^bv\left(t\right)dt$  

•  $x\left(a\right)+\int_a^bv\left(t\right)dt$  

•  $\int_a^b\left|v\left(t\right)\right|dt$  

•  $x\left(a\right)\ +\ \left(v\left(b\right)-v\left(a\right)\right)$  

Find the average velocity from on [a,b], given the function v(t).

•  $\frac{x\left(b\right)-x\left(a\right)}{b-a}$  

•  $\frac{v\left(b\right)-v\left(a\right)}{b-a}$  

•  $\frac{1}{b-a}\int_a^bv\left(t\right)dt$  

•  $\frac{v'\left(b\right)-v'\left(a\right)}{b-a}$  

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

To determine when a particle is at rest,

• Find where v(t) = 0

• Find where x(t) = 0

• Find where a(t) = 0

• Can't determine

To calculate the total displacement of a particle on [a,b], use the following:

•  $\int_a^bv\left(t\right)dt$  

•  $\int_a^b\left|v\left(t\right)\right|dt$  

•  $x\left(a\right)+\int_a^bv\left(t\right)dt$  

•  $v\left(b\right)-v\left(a\right)$