A speedboat is cruising at a speed of 11.8 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such that its speed during coasting is given by v = ve-ct, where v is the speed at time t, v, is the initial speed at t = 0, and c is a constant. At a time of t = 19.5 s after the engines are cut, the speed is 5.00 m/s. (a) What is the constant c (in s-¹) in the expression? s-1 (b) What is the speed (in m/s) at t = 40.0 s? m/s (c) Given the expression above for the speed at any time, which of the expressions below gives the speedboat's acceleration while coasting? a=-cV a = cv₁ a=-ce-ct a = ce-ct a = cv

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Chapter1: Units, Trigonometry. And Vectors
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A speedboat is cruising at a speed of 11.8 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such
that its speed during coasting is given by v = v₁e-ct, where v is the speed at time t, v, is the initial speed at t = 0, and c is a constant. At a time of t = 19.5 s after
the engines are cut, the speed is 5.00 m/s.
(a) What is the constant c (in s-¹) in the expression?
-1
(b) What is the speed (in m/s) at t = 40.0 s?
m/s
(c) Given the expression above for the speed at any time, which of the expressions below gives the speedboat's acceleration while coasting?
O
OO
a = -cv
a = CV i
a = -ce
a = ce
S
a = cv
-ct
-ct
Transcribed Image Text:A speedboat is cruising at a speed of 11.8 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the speedboat such that its speed during coasting is given by v = v₁e-ct, where v is the speed at time t, v, is the initial speed at t = 0, and c is a constant. At a time of t = 19.5 s after the engines are cut, the speed is 5.00 m/s. (a) What is the constant c (in s-¹) in the expression? -1 (b) What is the speed (in m/s) at t = 40.0 s? m/s (c) Given the expression above for the speed at any time, which of the expressions below gives the speedboat's acceleration while coasting? O OO a = -cv a = CV i a = -ce a = ce S a = cv -ct -ct
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