Check for Understanding: Particle Motion(Straight Line)

Acceleration is the rate of change of ________________.

• position
• velocity
• speed
• swag

What is velocity?

• the quickness of an object
• the location of an object
• acceleration
• speed in a specific direction

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?  

• v = 0
• v = 1
• v = -1
• v = -2

v(t)>0 means

• the particle is moving to the right
• the particle is moving to the left
• the particle has positive position
• the particle is at rest

Tags

CCSS.HSF.LE.B.5

Which of the following can be used to determine when a particle is at rest?

• x(t)=0
• v(t)=0
• a(t)=0

• A
• B
• C
• D

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

•  $\int_a^bv\left(t\right)dt$  

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

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

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

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

•  $\int_a^bv\left(t\right)dt$  

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

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

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

If  $v\left(t\right)=3t^2-4t$ and the particle's position is 13 when  $t=3$ , then what is the particle's position when  $t=4$ ? 

• 36

• 18

• 9

• 4

A particle is moving up and down the y-axis on the interval $0\le t\le10$ . The velocity of the particle is given by the equation $v\left(t\right)=\left(t-1\right)^{\frac{1}{3}}$ and the particle is at y=3 when t=0. Which of the following gives the position of the particle when t=5?

• $\int_0^5v\left(t\right)dt$

• $\int_0^5\left|v\left(t\right)\right|dt$

• $3+\int_0^5v\left(t\right)dt$

• $3+\int_0^5\left|v\left(t\right)\right|dt$