Particle Motion

A particle's speed is increasing when...
      I.   $v\left(t\right)$  and  $a\left(t\right)$  are opposite signs
     II.   $v\left(t\right)$  and  $a\left(t\right)$  are the same sign
    III.   $v\left(t\right)$  is positive and increasing
    IV.   $v\left(t\right)$  is negative and increasing
Select all that apply.

• I

• II

• III

• IV

How do you know when a particle changes direction?

• $v\left(t\right)$ and $a\left(t\right)$ are opposite signs

• $a\left(t\right)$ changes signs

• $v\left(t\right)=0$

• $v\left(t\right)$ changes signs

Tags

CCSS.HSF-LE.A.1C

If $x\left(t\right)=e^x+\ln x$ , then  $a\left(t\right)=$  ?

•  $e^x-\frac{1}{x^2}$  

•  $e^x+\frac{1}{x}$  

•  $e^x+\frac{1}{x^2}$  

•  $e^x-\frac{1}{x}$  

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

If a particle's position is given by $x\left(t\right)=\frac{2}{3}t^3-2t^2-16t+1$ , then the particle changes direction when  

•  $t=2$  

•  $t=3$  

•  $t=4$  

•  $t=5$  

Tags

CCSS.HSF-IF.C.7C

How do you find average acceleration?

• $\frac{\Delta a}{\Delta t}$

• $\frac{\Delta v}{\Delta t}$

• $f'\left(a\right)$

• $f'\left(v\right)$

Which of these could be the units of measurement for instantaneous velocity? Select all that apply.

• ft/sec

• ft/sec²

• inches

• ms^-1

The graph above represents the horizontal velocity of a particle. At what time does the particle reach it's maximum distance?

• $t=0.91$

• $t=7.081$

• $t=2.833$

• $t=3.733$

The velocity of a particle is given by the graph above. On the closed interval [0,7] when is the particle moving to the right?

• $\left(0,0.891\right)\cup\left(2.9,6.392\right)$

• $\left(0.891,2.9\right)\cup\left(6.392,7\right)$

• $\left(0,2.029\right)\cup\left(4.913,6.392\right)$

• $\left(2.9,6.392\right)$

Tags

CCSS.HSF.IF.B.4

Given the table for the velocity of a particle, what is the minimum number of times that the particle changed direction over the time interval [2,7]?

• 1

• 2

• 3

• 4