A yacht is cruising at a speed of 10.4 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the yacht such that its speed during -ct v,e, where v is the speed at time t, v 0, and c is a constant. At a time of t = 17.5 s after the engines are cut, the speed is is the initial speed at t coasting is given by v 5.00 m/s. What is the constant c (in s) in the expression? (a) 1 0.042 (b) What is the speed (in m/s) at t = 40.0 s? 1.95 m/s (c) Given the expression above for the speed at any time, which of the expressions below gives the yacht's acceleration while coasting? а3 —су -ct а3 се а %3D сV сV а%3 ct а %3D —се X\ Note the acceleration (in one direction) is the derivative of the speed. Take the derivative with respect to time and check the resulting expression carefully. How does it compare to the expression for the speed?

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A yacht is cruising at a speed of 10.4 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the yacht such that its speed during
-ct
v,e, where v is the speed at time t, v
0, and c is a constant. At a time of t = 17.5 s after the engines are cut, the speed is
is the initial speed at t
coasting is given by v
5.00 m/s.
What is the constant c (in s) in the expression?
(a)
1
0.042
(b) What is the speed (in m/s) at t = 40.0 s?
1.95
m/s
(c)
Given the expression above for the speed at any time, which of the expressions below gives the yacht's acceleration while coasting?
а3 —су
-ct
а3 се
а %3D сV
сV
а%3
ct
а %3D —се
X\
Note the acceleration (in one direction) is the derivative of the speed. Take the derivative with respect to time and check the resulting expression carefully. How does it
compare to the expression for the speed?
Transcribed Image Text:A yacht is cruising at a speed of 10.4 m/s in still water when it shuts off its engines and coasts to rest. The water exerts drag forces on the yacht such that its speed during -ct v,e, where v is the speed at time t, v 0, and c is a constant. At a time of t = 17.5 s after the engines are cut, the speed is is the initial speed at t coasting is given by v 5.00 m/s. What is the constant c (in s) in the expression? (a) 1 0.042 (b) What is the speed (in m/s) at t = 40.0 s? 1.95 m/s (c) Given the expression above for the speed at any time, which of the expressions below gives the yacht's acceleration while coasting? а3 —су -ct а3 се а %3D сV сV а%3 ct а %3D —се X\ Note the acceleration (in one direction) is the derivative of the speed. Take the derivative with respect to time and check the resulting expression carefully. How does it compare to the expression for the speed?
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