Worksheet 2.5 - Rates Of Change And Particle Motion I Worksheet (Page 7 of 8) in pdf

Worksheet 2.5 - Rates Of Change And Particle Motion I Worksheet Page 7

Calculus Maximus

WS 2.5: Rates of Change & Part Mot I

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12. The graph above shows the velocity,

v t , in miles per hour of a particle moving along the x-axis for

t ≤ ≤

hours. It consists of a semi circle and two line segments. Use the graph and your knowledge

of motion to answer the following questions.

t ≤ ≤

(a) At what time, 0

hours, is the speed of the particle the greatest?

t = ,

t = , or

t =

(b) At which of the times,

hours, is the acceleration of the particle greatest?

Justify.

t < <

hours is the particle moving to the left? Justify.

t < <

(d) Over what open time interval(s) 0

hours is the velocity of the particle increasing? Justify.

t < <

(e) Over what open time interval(s) 0

hours is the speed of the particle increasing? Justify.

t < <

(f) At what times on 0

is the acceleration of the particle undefined?

t ≤ ≤

(g) Find the area of the semicircle on the interval 0

bounded by the curve and the x-axis, then

t ≤ ≤

find the area of the triangle on the interval 4

bounded by the curve and the x-axis, and

t ≤ ≤

finally, find the area of the triangle on the interval 10

bounded by the curve and the x-axis.

If all of these areas were positive and added together, propose what quantity this might be in terms

t ≤ ≤

of the particle’s movement on 0

hours.

Page 7 of 8

Worksheet 2.5 - Rates Of Change And Particle Motion I Worksheet Page 7