(1)A motorist is traveling at 15 m/s when he sees
a deer in the road 44 m ahead.
If the maximum negative acceleration of
the vehicle is −6 m/s2, what is the maximum
reaction time of the motorist that will allow
him to avoid hitting the deer?
Answer in units of s.
(2)If his reaction time is 1.87223 s, how fast will
he be traveling when he reaches the deer?
Answer in units of m/s.
V^2 = Vo^2 + 2ad
To calculate the maximum reaction time (in seconds) that will allow the motorist to avoid hitting the deer, we need to consider the distance covered during the reaction time along with the maximum negative acceleration of the vehicle.
(1) To find the maximum reaction time:
1. First, calculate the distance covered during the reaction time using the formula:
Distance = Initial Velocity * Reaction Time
Given:
Initial Velocity (v0) = 15 m/s
Distance (s) = 44 m
Rearranging the formula, we have:
Reaction Time (t) = Distance / Initial Velocity
Substituting the values:
Reaction Time (t) = 44 m / 15 m/s = 2.93333 s
2. Next, determine the maximum acceleration. Since the maximum negative acceleration is given as -6 m/s^2, we can consider the magnitude of the acceleration without the negative sign.
3. Finally, the maximum reaction time of the motorist that will allow him to avoid hitting the deer is equal to the minimum of the reaction time calculated above and the time required for the vehicle to come to a stop with the maximum negative acceleration.
So, the maximum reaction time is 2.93333 s.
(2) To find the speed of the motorist when he reaches the deer:
1. Calculate the final velocity using the formula:
Final Velocity (v) = Initial Velocity (v0) + Acceleration * Reaction Time
Given:
Initial Velocity (v0) = 15 m/s
Acceleration (a) = -6 m/s^2 (negative value is considered when calculating final velocity)
Reaction Time (t) = 1.87223 s
Substituting the values:
Final Velocity (v) = 15 m/s + (-6 m/s^2) * 1.87223 s = 15 m/s - 11.23338 m/s = 3.76662 m/s
So, the motorist will be traveling at a speed of 3.76662 m/s when he reaches the deer.