The “reaction time” of the average automobile driver is about 0.7 s. (The reaction time is the interval between the perception of a signal to stop and the application of the brakes.) If an automobile can slow down with an acceleration of 12 ft/s^2 compute the total distance(in feet) covered in coming to a stop after a signal is observed from an initial velocity of 55 mi/h. Let 1 mi/h= 1.466 ft/s.

271 ft
327 ft
113 ft
414 f

I have absolutely no idea. If you could please show me what to do and how to get the answer and check my answer. That would be amazing! Thanks!

distance before slowing: 55 *1.466ft/sec*.7sec=56.1ft check that.

distance while braking:
vf^2=vo^2+2ad
d= (55*1.466)^2/(2*12)=271ft

add the two distances

Thanks so much! You’re the GOAT!

Wait so is 271 the answer?

check it. Taking my answer is ridiculous. I am trying to show you how to work it.

and the answer is, no it is not the answer. Add the distances.

What distances? 12 and what else?

12 and 55?

If so, is the answer 338 which is not an answer choice.

56.1ft +271= ???

so whats the answer?

To find the total distance covered in coming to a stop after a signal is observed, we need to consider two components: the distance covered during the reaction time and the distance covered while slowing down.

Let's break down the problem step by step:

1. Conversion: Convert the initial velocity from mi/h to ft/s.

Given: 1 mi/h = 1.466 ft/s
Initial velocity = 55 mi/h

To convert, multiply the initial velocity by the conversion factor:
Initial velocity in ft/s = 55 mi/h * 1.466 ft/s = 80.63 ft/s (rounded to two decimal places)

2. Reaction time distance: Calculate the distance covered during the reaction time.

Given: Reaction time = 0.7 s

Since the reaction time is the period between perceiving the signal and applying the brakes, the car continues moving with the initial velocity during this time.

Distance covered during reaction time = Initial velocity * Reaction time
Distance covered during reaction time = 80.63 ft/s * 0.7 s = 56.44 ft (rounded to two decimal places)

3. Slowing down distance: Calculate the distance covered while slowing down.

Given: Acceleration = 12 ft/s^2

We need to find the time it takes for the car to come to a complete stop. The formula for finding the time is given by:

Final velocity = Initial velocity + (Acceleration * Time)

Since the final velocity is 0 ft/s (car comes to a stop), we can rearrange the formula to solve for time:

Final velocity = Initial velocity + (Acceleration * Time)
0 ft/s = 80.63 ft/s + (12 ft/s^2 * Time)

Solving for Time:
80.63 ft/s = 12 ft/s^2 * Time
Time = 80.63 ft/s / 12 ft/s^2
Time = 6.72 s (rounded to two decimal places)

Now, we can calculate the distance covered while slowing down using the formula:

Distance covered while slowing down = (Initial velocity * Time) + (0.5 * Acceleration * Time^2)

Distance covered while slowing down = (80.63 ft/s * 6.72 s) + (0.5 * 12 ft/s^2 * (6.72 s)^2)
Distance covered while slowing down ≈ 541.57 ft (rounded to two decimal places)

4. Total distance: Sum up the distance covered during the reaction time and the distance covered while slowing down.

Total distance = Distance covered during reaction time + Distance covered while slowing down
Total distance = 56.44 ft + 541.57 ft
Total distance ≈ 597.01 ft (rounded to two decimal places)

Therefore, the total distance covered in coming to a stop after a signal is observed from an initial velocity of 55 mi/h is approximately 597.01 feet.

So, none of the given options (271 ft, 327 ft, 113 ft, 414 ft) match the correct answer.