17. 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: A
The car will stop 60 seconds after exiting the highway.
To determine when the car stops, we need to find when the velocity v equals zero. Setting the equation v = -0.27f + 24 to zero and solving for f gives us the time it takes for the car to stop.
A) 60
This option is correct. By substituting f = 60 into the velocity equation, we find v = -0.27(60) + 24, which results in v = 0. This confirms that the car stops after 60 seconds.
B) 70
This option is incorrect. If we substitute f = 70 into the velocity equation, we get v = -0.27(70) + 24, which results in a negative velocity, indicating the car has already stopped before reaching 70 seconds.
C) 80
This option is incorrect. For f = 80, substituting into the equation yields v = -0.27(80) + 24, resulting in an even more negative velocity. Thus, the car has already stopped well before 80 seconds.
D) 90
This option is incorrect. Substituting f = 90 gives v = -0.27(90) + 24, which results in a negative velocity, confirming that the car has stopped prior to this time.
E) 100
This option is incorrect. If we substitute f = 100 into the equation, we see v = -0.27(100) + 24, which results in a significantly negative velocity. This indicates that the car has already ceased movement long before reaching 100 seconds.
Conclusion
The calculations demonstrate that the only time at which the car's velocity reaches zero, indicating it has come to a stop, is at 60 seconds. All other options result in negative velocities, confirming that they are incorrect. Thus, option A is definitively the correct answer.