I really don't get why I am getting this question wrong? Please can you explain to me how to do this question step by step so that I can understand it please? :( i have been stuck on this question for quite a while now.

Determine the stopping distances for an automobile with an initial speed of 89 km/h and human reaction time of 2.0 s for the following:
(a) an acceleration a = -4.0 m/s2.
(b) a = -8.0 m/s2.

See previous post: Fri,10-13-13,2:36 AM.

To determine the stopping distance for an automobile with different accelerations, we need to consider two components: the distance covered during the driver's reaction time and the distance covered during the deceleration.

1. Distance during the driver's reaction time:
During the reaction time, the car continues to move with the initial speed before the driver applies the brakes. The formula to calculate the distance during this time is given by:
Distance_reaction = Initial speed × Reaction time

2. Distance during deceleration:
After the reaction time, the car starts decelerating until it comes to a stop. The formula to calculate the distance during this time is given by:
Distance_deceleration = (Initial speed × Distance_covered_per_second) + (0.5 × Acceleration × (Time_for_stopping)^2)

Now, let's calculate the stopping distances for the given initial speed, reaction time, and accelerations:

(a) Acceleration a = -4.0 m/s^2:
First, convert the initial speed from km/h to m/s:
Initial speed = 89 km/h × (1000 m/1 km) × (1 h/3600 s) = 24.72 m/s

Calculate the distance during the driver's reaction time:
Distance_reaction = Initial speed × Reaction time = 24.72 m/s × 2.0 s = 49.44 m

Calculate the distance during deceleration:
Time_for_stopping = -Initial speed / Acceleration
= -24.72 m/s / -4.0 m/s^2 = 6.18 s

Distance_deceleration = (Initial speed × Distance_covered_per_second) + (0.5 × Acceleration × (Time_for_stopping)^2)
= (24.72 m/s × 6.18 s) + (0.5 × -4.0 m/s^2 × (6.18 s)^2)
= 152.7672 m + 77.6144 m = 230.3816 m

Total stopping distance = Distance_reaction + Distance_deceleration
= 49.44 m + 230.3816 m = 279.8216 m

(b) Acceleration a = -8.0 m/s^2:
Using the same steps, we can calculate the stopping distance for this acceleration as well.

Initial speed = 24.72 m/s

Calculate the distance during the driver's reaction time:
Distance_reaction = Initial speed × Reaction time = 24.72 m/s × 2.0 s = 49.44 m

Calculate the distance during deceleration:
Time_for_stopping = -Initial speed / Acceleration
= -24.72 m/s / -8.0 m/s^2 = 3.09 s

Distance_deceleration = (Initial speed × Distance_covered_per_second) + (0.5 × Acceleration × (Time_for_stopping)^2)
= (24.72 m/s × 3.09 s) + (0.5 × -8.0 m/s^2 × (3.09 s)^2)
= 76.2528 m + 18.28818 m = 94.54098 m

Total stopping distance = Distance_reaction + Distance_deceleration
= 49.44 m + 94.54098 m = 143.98098 m

So, the stopping distances for (a) an acceleration of -4.0 m/s^2 is 279.8216 m, and for (b) an acceleration of -8.0 m/s^2 is 143.98098 m.