Answer:
The total traveled distance from when you first see the deer until you stop is 42 m.
Explanation:
Hi there!
The equation of position of the car while it is stopping is the following:
x = x0 + v0 · t + 1/2 · a · t²
Where:
x = position of the car after a time t.
x0 = initial position.
v0 = initial velocity.
a = acceleration.
t = time.
While the car travels at a constant speed (a = 0) its position will be given by the following equation:
x = v · t
Where v is the constant velocity.
First, let's convert km/h into m/s:
77.0 km/h · (1000 m/ 1km) · (1 h / 3600 s) = 21.4 m/s
Now, let´s calculate how much distance do you travel during the reaction time:
x = v · t
x = 21.4 m/s · 0.118 s
x = 2.53 m
You travel 2.53 m before hitting the brakes.
Now, let's see how much time it takes to stop the car. For that, we will use the equation of velocity of the car:
v = v0 + a · t
We have to find the time at which the car stops ( i.e., the value of t for which v = 0):
0 = v0 + a · t
Solving for t:
-v0/a = t
-21.4 m/s / -5.9 m/s² = t (notice that the acceleration is negative because its direction is opposite to the direction of the velocity).
t = 3.6 s
Now, let's find how much distance you travel in that time:
x = x0 + v0 · t +1/2 · a · t²
Let's consider the origin of the frame of reference at the point where you hit the brakes so that x0 = 0
x = 21.4 m/s · 3.6 s - 1/2 · 5.9 m/s² · (3.6 s)²
x = 39 m
The total traveled distance from when you first see the deer until you stop is (39 m + 2.53 m) 42 m.
