Derivatives and Particle Motion

A particle's speed is decreasing if

• it's acceleration is positive
• it's velocity is positive
• it's velocity and acceleration have the same sign
• it's velocity and acceleration have different signs

Tags

CCSS.HSN.VM.A.3

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

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

• 2
• 4
• 6
• 8

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

An objects distance from its starting point at time t is given by the equation

s(t) = t³ - 6t² - 4.

What is the speed of the object when its acceleration is 0?

• 12

• -24

• 22

• 2

A bug begins to crawl up a vertical wire at time t = 0.  The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction? 

• 2
• 4
• 6.5
• 7

Tags

CCSS.HSF.IF.B.4

Set up, but do not solve: If the position of Particle Bill is given by s(t) = x³ +2x - 7, how would you find when Bill is at rest?

• x³ +2x - 7 = 0

• 3x² + 2 = 0

• 6x = 0

• No work necessary. At rest when t = -7.

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)

• (0,1)

• (-∞,-1) $\cup$ (1,∞)

• (-1, 0) $\cup$ (1, $\infty$ )

f' is given, which could be f?

• A
• B
• C

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Given the graph of f'(x), where is f increasing?

• $\left(-\infty,\ -2\right)\cup\left(0,\ 2\right)\cup\left(3.5,\ \infty\right)$

• $\left(-3,\ -1\right)\cup\left(4,\ \infty\right)$

• $\left(-2,\ 0\right)\cup\left(2,\ 3.5\right)$

• $\left(-1,\ 2\right)\cup\left(2,\ \infty\right)$

Given the graph of f'(x), where is f concave up?

• $\left(-\infty,\ -2\right)\cup\left(0,\ 2\right)\cup\left(3.5,\ \infty\right)$

• $\left(-3,\ -1\right)\cup\left(4,\ \infty\right)$

• $\left(-2,\ 0\right)\cup\left(2,\ 3.5\right)$

• $\left(-1,\ 2\right)\cup\left(2,\ \infty\right)$