You're driving down the highway late one night at 22 m/s
m
/
s
when a deer steps onto the road 38 m
m
in front of you. Your reaction time before stepping on the brakes is 0.50 s
s
, and the maximum deceleration of your car is 10 m/s2
m
/
s
2
.
How much distance is between you and the deer when you come to a stop?
To find the distance between you and the deer when you come to a stop, we need to consider the total distance needed to stop the car.
First, let's calculate the distance covered during your reaction time. Given that your reaction time is 0.50 seconds and you're traveling at a speed of 22 m/s, the distance covered during your reaction time can be calculated using the formula:
Distance = Speed × Time
Distance = 22 m/s × 0.50 s
Distance = 11 m
So, during your reaction time, you would have traveled 11 meters.
Now let's calculate the distance covered while decelerating. To do this, we'll use the following formula:
Distance = (Initial Velocity)^2 / (2 × Acceleration)
Given that the initial velocity is 22 m/s and the acceleration is -10 m/s^2 (negative because we are decelerating), the distance covered while decelerating can be calculated as:
Distance = (22 m/s)^2 / (2 × -10 m/s^2)
Distance = 484 m^2/s^2 / (-20 m/s^2)
Distance = -24.2 m
Note that the negative sign indicates that the car is coming to a stop, so the displacement is in the opposite direction of the initial velocity.
Finally, to find the total distance between you and the deer when you come to a stop, we sum up the distance covered during your reaction time and the distance covered while decelerating:
Total Distance = Distance during reaction time + Distance while decelerating
Total Distance = 11 m + (-24.2 m)
Total Distance = -13.2 m
The negative value means that the deer is 13.2 meters behind you when you come to a stop. Therefore, there is no distance between you and the deer when you come to a stop.