Answer:
401.421 feet
Step-by-step explanation:
Given :[tex]v(t)=20 + 7cos t[/tex]
To Find : Find the distance traveled in 15 seconds by an object
Solution:
Equation :[tex]v(t)=20 + 7cos t[/tex]
where v is the speed and t is the time
Substitute t = 15
[tex]v(15)=20 + 7cos(15)[/tex]
[tex]v(15)=26.7614[/tex]
So, Speed = 26.7614 feet / second
Time = 15 seconds
Distance = [tex]Speed \times Time[/tex]
Distance = [tex]26.7614\times 15[/tex]
Distance = 401.421 feet
Hence the distance traveled in 15 seconds by an object moving with a velocity of[tex]v(t)=20 + 7cos t[/tex] feet per second is 401.421 feet
The distance traveled by the object at the given time is 401.4 ft
The given parameter:
time of motion, t = 15 s
velocity of the object, v(t) = 20 + 7 cos(t) ft/s
To find:
The velocity of the object at the given time is calculated as:
[tex]v(t) = 20 + 7cos(t) \\\\v(15) = 20 + 7cos(15)\\\\v = 20 + 7(0.9659)\\\\v = 26.76 \ ft/s[/tex]
The distance moved by an object is given by the following kinematic equation:
[tex]distance = speed \times \ time[/tex]
[tex]distance = 26.76 \ ft/s \ \times \ 15 \ s\\\\distance = 401.4 \ ft[/tex]
Thus, the distance moved by the object is 401.4 ft
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