What is the maximum reaction time to avoid hitting a deer on the road?

[jello]

a car is moving at 56km/h when a deer jumps onto the road 65m ahead. after a reaction time of t seconds, the driver applies the brakes to produce an acceleration of -3.0m/s^2. what is the maximum reaction time allowed if the car is to avoid hitting the deer?

 

[Siracuse]

It may be "fun" to solve that kinematics problem, but why exactly did you post here? If you have any doubts or want help to solve the problem, you have to show some previous effort on trying to solve the exercise (forum rule).

 

[ogb p]

Hello! This is a great kinematics problem that involves both distance and time. To solve this problem, we can use the kinematic equation: d = v0t + 1/2at^2, where d is the distance, v0 is the initial velocity, a is the acceleration, and t is the time.

In this case, we know that the car is moving at an initial velocity of 56km/h, which we can convert to meters per second (m/s) by dividing by 3.6. This gives us an initial velocity of 15.56 m/s. We also know that the deer is 65m ahead of the car, so d = 65m.

To avoid hitting the deer, the car needs to come to a complete stop before reaching the deer. This means that the final velocity (vf) must be 0 m/s. We also know that the acceleration is -3.0m/s^2, as given in the problem.

Plugging in these values into the kinematic equation, we get:

0 = 15.56t + 1/2(-3.0)t^2

Simplifying, we get:

0 = 15.56t - 1.5t^2

To solve for t, we can use the quadratic formula: t = (-b ± √(b^2-4ac))/2a, where a = -1.5, b = 15.56, and c = 0.

Solving for t, we get two solutions: t = 0 and t = 10.37 seconds.

The first solution, t = 0, means that the car would stop immediately without any reaction time. However, this is not possible in real life as it takes time for the driver to react and apply the brakes.

Therefore, the maximum reaction time allowed for the car to avoid hitting the deer is t = 10.37 seconds. Any longer than this and the car would not be able to stop before reaching the deer.

I hope this helps solve the problem and emphasizes the importance of reaction time in avoiding accidents. Thank you for the fun kinematics problem!