Final answer:
To determine if you will smash into the back of the car stopped in front of you, we need to calculate the stopping distance and compare it to the distance to the car. During your reaction time, the car will continue to move at a constant velocity of 24 m/s. After the brakes have been applied, the car slows down at a rate of 8.0 m/s².
Step-by-step explanation:
To determine if you will smash into the back of the car stopped in front of you, we need to calculate the stopping distance and compare it to the distance to the car. First, let's calculate the stopping distance during your reaction time. During the reaction time, the car will continue to move at a constant velocity of 24 m/s, so the distance traveled during the reaction time is:
Distance = Velocity x Time = 24 m/s x 0.80 s = 19.2 m
Next, let's calculate the stopping distance after the brakes have been applied. The car slows down at a rate of 8.0 m/s², so the stopping distance can be calculated using the equation:
Stopping Distance = (Velocity² - Initial Velocity²) / (2 x Acceleration) = (0² - 24²) / (2 x -8.0 m/s²) = 72 m
Finally, we add the distance traveled during the reaction time and the stopping distance:
Total Distance = Distance during reaction time + Stopping Distance = 19.2 m + 72 m = 91.2 m
Since the car stopped 30 m in front of you and the total distance required to stop is 91.2 m, you will indeed smash into the back of the car stopped in front of you.