Unit 4 Review of Context Applications

A particle moves along the x-axis so that its position at time t is given by $x\left(t\right)=t^2-6t+5$ .  For what value of t is the velocity of the particle zero?

• 1

• 2

• 3

• 4

• 5

A particle moves along a line so that at time t, where  $0\le t\le\pi$ , its position is given by  $s\left(t\right)=-2\cos t-\frac{t^2}{2}+10$  .  What is the velocity of the particle when its acceleration is zero?

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{6}$  

•  $\sqrt{3}-\frac{\pi}{3}$  

•  $1-\frac{\pi}{6}$  

• No values

• 1

• 3

• 5

• 1 and 3

• -45

• -30

• -15

• -10

• -5

• The ant is at rest at t=0 and t=3

• The ant changes direction at t=3

• The acceleration of the ant is always positive

• The ant is speeding up when t=4

• The acceleration of the ant is 0 at t=1

• The ant is moving the fastest at t=1 and t=4
  

• The ant is speeding up when t=2

• At t=1, the ant is moving to the right

• The average acceleration of the ant is positive over the interval [0,4]

The table shows oil production for 2001-2007 (t=1 represents 2001). Estimate P'(2).

• 0.15 million gallons/day

• 0.15 million gallons/day/year

• 0.10 million gallons/day/year

• 0.10 million gallons/day

The number of iPods sold by Apple each year from 2004 through 2007 can be approximated by  $f\left(t\right)=-t^2+20t+3$  in millions of iPods where t=0 represents 2004.  Is the number of iPods sold in 2006 increasing or decreasing? 

• Increasing

• Decreasing

• At the 6th year, the lion population grows at a rate of 12 lions

• At the 6th year, the lion population grows at a rate of 12 lions per year

• The lion population grows at a rate of 12 lions per 6 years

• At the 6th year, there were 12 lions in the reserve

Water is filling a pool. The function W gives the pool's water level (in meters) after t minutes. What is the best interpretation of the statement "The slope of the line tangent to the graph of W at t=5 is equal to 0.1."

• At the 5th minute, the pool is being filled at a rate of 0.1 meters per minute

• At the 5th minute, the pool's water level is 0.1 meters

• At the 5th minute, the pool is being filled at a rate of 0.1 minutes per meter