Question 346954: I am having trouble in answering all questions in my assignment.Please help me it is due tomorrow.We are noe in calculus.A truck travelling along a straight section of highway, on a wet evening, braked suddenly to avoild blinky Bill who had wandered onto the road off in the distance.The reducing velocity of the truck under braking,v, in metres per second,is modelled by the equation:
v=30e^-t/2 -5
where t is the number of seconds after the brakes were applied.Assume the truck held its line under braking conditions.
Question2
a. Find a fully simplified expression for v'(t)
b. Sketch a graph od v'(t) over the domain [0,10)
c. Explain what the derivative expression and sketch represents in terms of the braking situation?
d. Evaluate v'(0) and v'(2) explain the relevance of these values to the model.
Question 3
a. Find an expression for the distance traveled,s(t) after t seconds.
b. Sketch a grapgh of s(t) over the domain [0,10).
c. Discuss the limitation of this function as a model for the distance covered after braking.
d. Poor Blinky was 30m down the highway whe the brakes were applied. He was dazzled by the lights of the truck and froze to the spot.Show why our favorite koala was in a spot of bother.
e. How fast was the truck going when it struck Blinky?
f. What was the minimum distance Blinky could have been standing to avoid contact?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A truck travelling along a straight section of highway, on a wet evening, braked suddenly to avoid blinky Bill who had wandered onto the road off in the distance.The reducing velocity of the truck under braking,v, in metres per second,is modelled by the equation:
v=30e^(-t/2) -5
where t is the number of seconds after the brakes were applied.
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Assume the truck held its line under braking conditions.
Question2
a. Find a fully simplified expression for v'(t)
v'(t) = 30(-1/2)e^(-t/2)
v'(t) = -15*e^(-t/2)
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b. Sketch a graph of v'(t) over the domain [0,10)
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c. Explain what the derivative expression and sketch represents in terms of the braking situation?
Heavy braking initially; then gradually reduced bracking.
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d. Evaluate v'(0) and v'(2) explain the relevance of these values to the model.
v'(0) = -15 :::: deceleration is initially 15 ft/sec^2
v'(2) = -15e^-1 :::: deceleration is 5.5 ft/sec^2 at time = 2 seconds
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Question 3
a. Find an expression for the distance traveled, s(t) after t seconds.
Integrate v(t) to get s(t)
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b. Sketch a grapgh of s(t) over the domain [0,10).
c. Discuss the limitation of this function as a model for the distance covered after braking.
d. Poor Blinky was 30m down the highway whe the brakes were applied. He was dazzled by the lights of the truck and froze to the spot.Show why our favorite koala was in a spot of bother.
e. How fast was the truck going when it struck Blinky?
f. What was the minimum distance Blinky could have been standing to avoid contact?
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Cheers,
Stan H.
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