Diego runs back and forth along a straight track. During the time interval 0sts 30 seconds, 200 sin Diego's velocity, in feet per second, is modeled by the function v given by v(t) = a) What is the first time, t4, the Diego changes direction? Find Diego's average velocity over the time interval 0sist. b) At time t = 30, how far is Diego from his position at time t = 0?

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Chapter1: Units, Trigonometry. And Vectors
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Diego runs back and forth along a straight track. During the time interval 0<t< 30 seconds,
200 sin
Diego's velocity, in feet per second, is modeled by the function v given by v(t) =
t+1
a) What is the first time, t1, the Diego changes direction? Find Diego's average velocity over
the time interval 0 stst.
b) At time t = 30, how far is Diego from his position at time t = 0?
c) Find the total distance that Diego runs during the 30 seconds from the time t = 0 to time
t = 30.
d) Let a(t) represent Diego's acceleration during the time interval 0 <t < 30 seconds. Using
correct units, explain the meaning of f" a(t)dt in the context of the problem. Find the value
of " a(t)dt.
Transcribed Image Text:Diego runs back and forth along a straight track. During the time interval 0<t< 30 seconds, 200 sin Diego's velocity, in feet per second, is modeled by the function v given by v(t) = t+1 a) What is the first time, t1, the Diego changes direction? Find Diego's average velocity over the time interval 0 stst. b) At time t = 30, how far is Diego from his position at time t = 0? c) Find the total distance that Diego runs during the 30 seconds from the time t = 0 to time t = 30. d) Let a(t) represent Diego's acceleration during the time interval 0 <t < 30 seconds. Using correct units, explain the meaning of f" a(t)dt in the context of the problem. Find the value of " a(t)dt.
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