26. The velocity of a car f seconds after it exits a highway is given by v = -0.27f + 24. How many seconds after exiting will the car stop?
Answer: B
The car will stop after 90 seconds.
To determine when the car stops, we need to find when the velocity \( v \) equals zero. Setting the equation \( -0.27f + 24 = 0 \) and solving for \( f \) gives us \( f = 90 \) seconds.
A) 89
Choosing 89 seconds would imply that the velocity is not yet zero, as substituting \( f = 89 \) into the equation results in a positive velocity. Therefore, this option is incorrect.
B) 90
This option is correct because substituting \( f = 90 \) into the velocity equation yields \( v = -0.27(90) + 24 = 0 \). This indicates that the car comes to a complete stop at exactly 90 seconds after exiting the highway.
C) 100
At 100 seconds, substituting \( f = 100 \) into the equation results in a negative velocity \( v = -0.27(100) + 24 = -3 \), which indicates the car has already stopped and is moving backward. Thus, this option is not correct.
D) 110
Similarly, at 110 seconds, substituting \( f = 110 \) into the equation gives \( v = -0.27(110) + 24 = -6.7 \). This further confirms that the car has already stopped and is traveling in the opposite direction, making this option incorrect as well.
Conclusion
The correct answer is 90 seconds, as it represents the point at which the car's velocity reaches zero, indicating it has stopped. All other options fail to provide a valid stopping time, either suggesting that the car is still moving or has already begun to reverse.