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,10-11-13,2:36 AM.

Of course, I'd be happy to help you understand this question step by step!

To determine the stopping distances for an automobile, we need to consider two main factors: the reaction time and the acceleration.

1. Reaction time:
The reaction time refers to the time it takes for a driver to react and apply the brakes after perceiving a situation that requires them to stop. In this question, the given reaction time is 2.0 seconds.

2. Initial speed:
The initial speed of the automobile is given as 89 km/h. Before we can proceed with the calculations, we need to convert this speed to meters per second (m/s) since the acceleration is supplied in meters per second squared (m/s^2). To convert km/h to m/s, divide the speed by 3.6:

89 km/h ÷ 3.6 = 24.72 m/s (rounded to two decimal places)

Now we have the initial speed in m/s, which is 24.72 m/s.

3. Stopping distance formula:
The stopping distance can be calculated using the formula:

Stopping distance = (Initial speed × Reaction time) + (0.5 × Acceleration × Reaction time^2)

Now let's calculate the stopping distances for each scenario, using the given information.

(a) For an acceleration of -4.0 m/s^2:
Substitute the values into the formula:
Stopping distance = (24.72 m/s × 2.0 s) + (0.5 × -4.0 m/s^2 × (2.0 s)^2)

Calculating the expression:
Stopping distance = (49.44 m) + (-4.0 m/s^2 × 4.0 s^2)
Stopping distance = 49.44 m - 32.0 m
Stopping distance = 17.44 m

Therefore, the stopping distance for an acceleration of -4.0 m/s^2 is 17.44 meters.

(b) For an acceleration of -8.0 m/s^2:
Substitute the values into the formula:
Stopping distance = (24.72 m/s × 2.0 s) + (0.5 × -8.0 m/s^2 × (2.0 s)^2)

Calculating the expression:
Stopping distance = (49.44 m) + (-8.0 m/s^2 × 4.0 s^2)
Stopping distance = 49.44 m - 64.0 m
Stopping distance = -14.56 m

Therefore, the stopping distance for an acceleration of -8.0 m/s^2 is -14.56 meters.

After calculating the stopping distances for both scenarios, we can conclude that when the acceleration is -4.0 m/s^2, the stopping distance is 17.44 meters, and when the acceleration is -8.0 m/s^2, the calculated stopping distance is -14.56 meters. Note that a negative stopping distance suggests that the object did not come to a complete stop, but rather reversed its direction of motion.

I hope this step-by-step explanation helps you understand the question and concept better. If you have any further questions, feel free to ask!