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.

Vo=85000m/h = 85000m/3600s = 23.61 m/s.

a. V = Vo + a*t
T = (V-Vo)/a + Tr
T = (0-23.61)/-4 + 2s = 7.9 s = Stopping time.
d = Vo*t + 0.5a*t^2
d = 23.61*7.9 + 0.5*-4*7.9^2 = 61.7m

b. T = (0-23.61)/-8 + 2s = 4.95 s.
d=23.61*4.95 + 0.5*(-8)*4.95^2=18.86 m.

CORRECTION:

Vo=89,000m/1h = 89000/3600s = 24.72 m/s

a. V = Vo + va*t
T = (V-V0)/a + Tr
T = (0-24.72)/-4 + 2s.=8.18 s.=Stopping
time.
d = Vo*t + 0.5a*t^2
d=24.72*8.18 + 0.5*(-40*8.18*2=68.38 m.

b. T = (0-24.72)/-8 + 2s = 5.09 s.
d=24.72*5.09 + 0.5*(-8)*5.09^2= 22.19 m.

Sure, I'd be happy to help you step by step.

To determine the stopping distance, we need to consider two main components: the distance traveled during the human reaction time, and the distance traveled during the deceleration period.

1. Calculate the distance traveled during the reaction time:
During the human reaction time, the car continues to move forward at its initial speed before the brakes are engaged. The formula to calculate the distance during this time is:

distance_reaction = initial_speed * reaction_time

In this case, the initial speed is given as 89 km/h. To convert it to m/s, divide by 3.6 because 1 km/h is equal to 1/3.6 m/s. So, the initial speed is 89 km/h / 3.6 = 24.7 m/s. The reaction time is given as 2.0 s.

distance_reaction = 24.7 m/s * 2.0 s = 49.4 m

So, the distance traveled during the reaction time is 49.4 meters.

2. Calculate the distance traveled during deceleration:
The car is now decelerating with the given acceleration. We'll use the formula of motion to calculate this distance:

distance_deceleration = (final_speed^2 - initial_speed^2) / (2 * acceleration)

(a) For acceleration a = -4.0 m/s²:
The final speed is 0 m/s since the car stops at the end. Therefore:

distance_deceleration_a = (0^2 - 24.7^2) / (2 * (-4.0)) = 306.88 m

(b) For acceleration a = -8.0 m/s²:
Again, the final speed is 0 m/s. Therefore:

distance_deceleration_b = (0^2 - 24.7^2) / (2 * (-8.0)) = 153.44 m

So, the distance traveled during the deceleration for (a) is 306.88 meters, and for (b) is 153.44 meters.

3. Calculate the total stopping distance:
To find the total stopping distance, we add the distances traveled during the reaction time and the deceleration:

total_stopping_distance = distance_reaction + distance_deceleration

(a) For acceleration a = -4.0 m/s²:
total_stopping_distance_a = 49.4 m + 306.88 m = 356.28 m

(b) For acceleration a = -8.0 m/s²:
total_stopping_distance_b = 49.4 m + 153.44 m = 202.84 m

So, the total stopping distance for (a) is 356.28 meters, and for (b) is 202.84 meters.

I hope this step-by-step explanation helps you understand how to approach this question. Let me know if you have any further questions!