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.

v=89 km/h=89000/3600= 24.7 m/s.

The distance covered during the reaction time is
s₁=v₀t₁=24.7•0.2=49.4 m
The distance covered during braking s₂
s₂=v₀t₂-at₂²/2
v=v₀-at₂
v=0 =>
t₂=v₀/a
s₂=v₀²/2a =24.7²/2•4=76.3 m
s=s₁+s₂ =49.4+76.3 =125.7 m

Of course! I'll be glad to explain the steps to solve this question.

To determine the stopping distances given the initial speed, human reaction time, and acceleration, we need to use the equations of motion. The key equation we'll be using is the equation for the stopping distance, which is:

d = v₀t + (1/2)at²

Where:
- d is the stopping distance,
- v₀ is the initial speed,
- t is the human reaction time, and
- a is the acceleration.

Let's solve part (a) of the question first:

(a) For an acceleration a = -4.0 m/s², we'll use the given values:
- v₀ = 89 km/h
- t = 2.0 s
- a = -4.0 m/s²

Step 1: Convert the initial speed from km/h to m/s.
To do this, we need to remember that 1 km/h is equal to 1000 m/3600 s.

v₀ = 89 km/h * (1000 m/3600 s)
v₀ = 24.7 m/s (rounded to one decimal place)

Step 2: Plug in the values into the equation for the stopping distance.

d = v₀t + (1/2)at²
d = (24.7 m/s)(2.0 s) + (1/2)(-4.0 m/s²)(2.0 s)²

Simplifying further:
d = 49.4 m - 8.0 m
d = 41.4 m

So, the stopping distance is 41.4 meters.

Now, let's move on to part (b) of the question:

(b) For an acceleration a = -8.0 m/s², we'll use the same values for v₀ and t.
- v₀ = 24.7 m/s
- t = 2.0 s
- a = -8.0 m/s²

Step 1: Repeat step 2 from part (a) using the new value of the acceleration.

d = v₀t + (1/2)at²
d = (24.7 m/s)(2.0 s) + (1/2)(-8.0 m/s²)(2.0 s)²

Simplifying further:
d = 49.4 m - 16.0 m
d = 33.4 m

So, the stopping distance is 33.4 meters for an acceleration of -8.0 m/s².

I hope this explanation helps you understand the steps and solve the question! Let me know if you have any other questions.