A motorist traveling at 15 m/s encounters a
deer in the road 46 m ahead.
If the maximum acceleration the vehicle’s
brakes are capable of is −7 m/s2, what is the
maximum reaction time of the motorist that
will allow her or him to avoid hitting the deer?
To determine the maximum reaction time of the motorist, we need to consider the distance they will travel while reacting to avoid hitting the deer.
Let's break down the problem:
1. The motorist is traveling at a constant velocity of 15 m/s.
2. The motorist needs to stop the vehicle to avoid hitting the deer, which requires applying the maximum brake acceleration of -7 m/s^2.
3. The motorist's reaction time needs to be determined.
We can calculate the distance the motorist will travel while reacting by using the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, the initial velocity is 15 m/s and the acceleration is -7 m/s^2. However, since we want to find the maximum reaction time, we assume the motorist starts braking right at the moment they see the deer, so the initial velocity becomes 0.
Let's plug in the values into the formula and solve for time:
distance = 0 * t + (1/2) * (-7) * t^2
46 = -3.5t^2
Rearranging the equation:
t^2 = -(46 / -3.5)
t^2 = 13.14
Taking the square root of both sides:
t ≈ √13.14
t ≈ 3.62 s (rounded to two decimal places)
Therefore, the maximum reaction time of the motorist that will allow them to avoid hitting the deer is approximately 3.62 seconds.