You are driving at 28.0 m/s on i-5 south through the terwilliger curves. you notice a deer jump onto the highway at a location 62.0 m in front of your car. you first react to the event, then slam on your brakes and accelerate at -8.10 m/s2, and ultimately stop just in front of the frozen deer.
what is your reaction time?

Your reaction time is 0.486 s

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

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