Answer:
Your reaction time is 0.486 s
Step-by-step explanation:
Hi there!
The equation of velocity of the car is the following:
v = v0 + a · t
Where:
v = velocity at time t.
v0 = initial velocity.
a = acceleration.
t = time.
When the car stops, the velocity is zero. So, let´s find the time it takes the car to stop after pushing the brakes:
v = 0
0 = v0 + a · t
0 = 28.0 m/s - 8.10 m/s² · t
-28.0 m/s / -8.10 m/s² = t
t = 3.46 s
Now let´s calculate the distance traveled by the car during this time using this equation:
x = x0 + v0 · t + 1/2 · a · t²
Where:
x = position of the car at time t.
x0 = initial position.
v0 = initial velocity.
a = acceleration.
t = time.
Let´s consider the origin of the system of reference at the point where you hit the brakes so that x0 = 0.
x = v0 · t + 1/2 · a · t²
x = 28.0 m/s · 3.46 s - 1/2 · 8.10 m/s² · (3.46 s)²
x = 48.4 m
Then, the distance traveled before you hit the brakes is (during the time it takes you to react):
62.0 m - 48.4 m = 13.6 m
At constant velocity, the traveled distance is calculated as follows:
x = v · t
Solving for t:
x/v = t
13.6 m / 28.0 m/s = t
t = 0.486 s
Your reaction time is 0.486 s