How do I solve this?

Traveling at 60. mi/hr you see a dog in the road. Your reaction time to hit the brakes is 0.75 seconds and you can decelerate at 7.9 m/s^2. (1 mile = 1609 meters)

A) How far do you travel from the moment you see the dog until the moment you hit the brakes?

B) Over what distance does the car come to a stop once you hit the brakes?

C) What is the total stopping distance from the moment you see the dog?

a. distance=speed*time change mi/hr to m/s

b. vf^2=Vi^2+2ad a=-7.9m/s^2 solve for distance d.

c. total ? add distances in a and b.

gfsd

To solve this problem, we will break it down into three parts:

A) Calculate the distance traveled from the moment you see the dog until the moment you hit the brakes.
B) Calculate the distance required for the car to come to a stop once you hit the brakes.
C) Find the total stopping distance from the moment you see the dog.

Let's start with part A:

A) To calculate the distance traveled from the moment you see the dog until the moment you hit the brakes, we need to multiply the reaction time by the initial velocity.

The formula for distance is given by: distance = speed × time

Given:
Reaction time (t) = 0.75 seconds
Initial velocity (speed) = 60 miles/hour = (60 miles/hour) × (1609 meters/1 mile) × (1 hour/3600 seconds)

To convert the velocity from miles/hour to meters/second, we need to multiply by the conversion factors: 1609 meters/1 mile and 1 hour/3600 seconds.

Substituting the values:

Initial velocity (speed) = (60 miles/hour) × (1609 meters/1 mile) × (1 hour/3600 seconds)
= 26.82 meters/second

Now, we can calculate the distance:

Distance = Initial velocity × Reaction time
= 26.82 meters/second × 0.75 seconds
= 20.115 meters

Therefore, from the moment you see the dog until the moment you hit the brakes, you travel a distance of approximately 20.115 meters.

Now, let's move on to part B:

B) To calculate the distance required for the car to come to a stop once you hit the brakes, we need to use the formula for distance:

Distance = (Final velocity^2 - Initial velocity^2) / (2 × acceleration)

Given:
Initial velocity = 0 meters/second (since you hit the brakes)
Acceleration = -7.9 m/s^2 (negative because it is deceleration)

Substituting the values:

Distance = (0 m/s^2 - (26.82 m/s)^2) / (2 × (-7.9 m/s^2))
= 720.09 meters / (2 × (-7.9))
= 720.09 meters / (-15.8)
≈ -45.58 meters (Note: The negative sign indicates direction)

Therefore, the car comes to a stop over a distance of approximately 45.58 meters.

Finally, let's calculate part C:

C) The total stopping distance is the sum of the distances calculated in part A and part B:

Total stopping distance = Distance traveled until hitting the brakes + Distance required to come to a stop
= 20.115 meters + 45.58 meters
≈ 65.695 meters

Therefore, the total stopping distance from the moment you see the dog is approximately 65.695 meters.