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 90 seconds after exiting the highway.

To determine when the car stops, we set the velocity equation (v = -0.27f + 24) to zero and solve for (f). This leads us to (0 = -0.27f + 24), resulting in (f = 90) seconds.

A (89) YOUR ANSWER

If the car were to stop at 89 seconds, we would calculate the velocity at that time as (v = -0.27(89) + 24), which yields a positive velocity. Therefore, the car would still be in motion at 89 seconds, confirming this option is incorrect.

B (90) CORRECT

At 90 seconds, substituting (f) into the velocity equation gives (v = -0.27(90) + 24 = 0). This confirms that the car comes to a complete stop at exactly 90 seconds, validating this option as the correct answer.

C (100) YOUR ANSWER

If we calculate the car's velocity at 100 seconds, we find (v = -0.27(100) + 24 = -3), indicating the car would be moving in the opposite direction at that time. Hence, this option is not when the car stops.

D (110) YOUR ANSWER

At 110 seconds, the velocity would be calculated as (v = -0.27(110) + 24 = -6.7), which again shows the car is moving backward. Therefore, this choice is also incorrect since the car does not stop at this time.

Conclusion

The solution to when the car stops is determined by finding when the velocity equation equals zero. The calculations show that the car stops precisely at 90 seconds after exiting the highway. Other choices indicate either continued motion or movement in the opposite direction, reaffirming that 90 seconds is the only correct answer.

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 90 seconds after exiting the highway.

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