Unit 4: Contextual Applications of Differentiation

Question 1

Position Symbol

Answer 1

s(t)

Question 2

Velocity Symbol

Answer 2

v(t) = s’(t)

Question 3

Acceleration Symbol

Answer 3

a(t) = v’(t) = s(t)

Question 4

Particle changing direction

Answer 4

velocity changes sign –> find v(t) = 0

Question 5

Velocity quantity

Answer 5

vector quantity: magnitude and direction

Question 6

Velocity and Acceleration signs

Answer 6

Same sign = increasing speed
Different signs = decreasing speed
+ = right
- = left

Question 7

Distance vs. Displacement

Answer 7

Distance = the sum of the distances traveled on each subinterval without a change of direction [find where the v(t) changes sign, absolute values of the differences and add them up]
Displacement = the difference between its terminal and initial positions.

Question 8

Describing the particle’s motion

Answer 8

state the interval, the direction, incr./decr. speed, and the reason.

ex. for 0<t<2, moving right, speed decreases because v(t)>0 and a(t)<0.

Question 9

Related Rates Tip

Answer 9

never substitute for things that change until after you take derivatives!

Question 10

related rates triangles

Answer 10

x^2 + y^2 = z^2