SOLUTION: hello everyone.I need your help with my Calculus assignment. It is due today.Please help me.The right equation is,v=-5+30e^-t/2 A truck travelling along a straight section of high

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Question 347251: hello everyone.I need your help with my Calculus assignment. It is due today.Please help me.The right equation is,v=-5+30e^-t/2
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=-5+30e^-t/2
where t is the number of seconds after the brakes were applied.Assume the truck held its line under braking conditions.
Questions:
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 Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
s%28t%29=int%28v%28t%29%2Cdt%29
s%28t%29=int%28%28-5%2B30e%5E%28-0.5t%29%29%2Cdt%29
s%28t%29=-5-%2830%2F%281%2F2%29%29e%5E%28-0.5t%29%2BC
s%28t%29=-5-60e%5E%28-0.5t%29%2BC
When t=0, s(0)=0.
s%280%29=-5-60%2BC=0
C=65
s%28t%29=-5-60e%5E%28-0.5t%29%2B651
highlight%28s%28t%29=60-60e%5E%28-0.5t%29%29
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b)
graph%28300%2C300%2C-2%2C12%2C-10%2C90%2C60-60e%5E%28-0.5x%29%2C60%2C30%29
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c)I'll leave that part to you.
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d)Oh no. The truck doesn't stop until s=60m (the green line).
Poor Blinky never had a chance (he was standing at the blue line).
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e)Find t when s%28t%29=30.
60-60e%5E%28-0.5t%29=30
-60e%5E%28-0.5t%29=-30
e%5E%28-0.5t%29=1%2F2
-0.5t=ln%281%2F2%29
t=-2%2Aln%281%2F2%29
t=-2%2A%28-0.693%29
t=1.386seconds
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Now find v%281.386%29.
v%28t%29=-5%2B30e%5E%28-0.5t%29
I'll leave that to you to finish.
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f) Blinky needed to be at a distance of greater than 60m.