2. A particle moves along the x-axis so that its velocity at any time t 2 0 is given by v(t) = 3t² – 2t + 4. when t = 2, the position of the particle is X = 5. Here is a graph of this velocity: V 70 60 50 40 30 20 10 t a. Using 8 rectangles of equal width and left-hand endpoints, estimate the distance traveled by the particle between t = 1 and t = 5. %3D b. Is your answer to part a an underestimate, an overestimate, or exactly correct? c. Write a polynomial expression for the position of the particle at any time t 2 0. d. Use your expression from part c to find the total distance traveled by the particle between t = 1 and t = 5. (Note – your answers to a and d should be close.)

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2. A particle moves along the x-axis so that its velocity at any time t 2 0 is given by
v(t)
3t – 2t + 4. when t = 2, the position of the particle is X = 5.
Here is a graph of this velocity:
V
70
60
50
40
30
20
10
3
t
a. Using
8.
rectangles of equal width and left-hand endpoints, estimate the distance
traveled by the particle between t = 1 and t = 5.
b. Is your answer to part a an underestimate, an overestimate, or exactly correct?
c. Write a polynomial expression for the position of the particle at any time t 2 0.
d. Use your expression from part c to find the total distance traveled by the particle
between t = 1 and t = 5. (Note – your answers to a and d should be close.)
Transcribed Image Text:2. A particle moves along the x-axis so that its velocity at any time t 2 0 is given by v(t) 3t – 2t + 4. when t = 2, the position of the particle is X = 5. Here is a graph of this velocity: V 70 60 50 40 30 20 10 3 t a. Using 8. rectangles of equal width and left-hand endpoints, estimate the distance traveled by the particle between t = 1 and t = 5. b. Is your answer to part a an underestimate, an overestimate, or exactly correct? c. Write a polynomial expression for the position of the particle at any time t 2 0. d. Use your expression from part c to find the total distance traveled by the particle between t = 1 and t = 5. (Note – your answers to a and d should be close.)
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