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?

Rationale

The car will stop 60 seconds after exiting the highway.

To find when the car stops, we set the velocity equation (v = -0.27f + 24) to zero and solve for (f). This gives us (0 = -0.27f + 24), leading to (f = 60) seconds, indicating that the car comes to a stop at this time.

A (60) CORRECT

This choice is correct because when we solve the equation for when the velocity becomes zero, we find (f = 60). This is the exact moment when the car ceases to move, as calculated from the equation provided.

B (70) YOUR ANSWER

This option is incorrect because if we substitute (f = 70) into the velocity equation (v = -0.27(70) + 24), we find (v = -0.27 * 70 + 24 = 18.1), indicating that the car is still moving at a speed of 18.1 units at this time.

C (80) YOUR ANSWER

Similarly, substituting (f = 80) into the equation yields (v = -0.27(80) + 24 = 10.4). This calculation shows that the car is still in motion with a velocity of 10.4 units, thus it has not yet stopped.

D (90) YOUR ANSWER

For (f = 90), the calculation gives (v = -0.27(90) + 24 = 2.7). This result indicates that the car is still moving with a low speed of 2.7 units, showing it has not reached a complete stop.

E (100) YOUR ANSWER

Finally, substituting (f = 100) results in (v = -0.27(100) + 24 = -3). A negative velocity indicates that the car has actually reversed direction, further confirming that it did not stop at this time.

Conclusion

The car will stop after 60 seconds as derived from the velocity equation. While other choices reflect moments when the car is still in motion or even reversing, only 60 seconds corresponds to a velocity of zero. This analysis reinforces the importance of understanding how to manipulate linear equations to determine motion-related variables accurately.

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?

The car will stop 60 seconds after exiting the highway.

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