If you are traveling at 30 m/s (about 60 mph) and see a deer in the middle of the road, how far will you travel before you even hit the brakes? Your reaction time is 6.904 m/s
reaction distance = speed * reaction time
To determine how far you will travel before hitting the brakes, you need to consider two factors: the distance traveled during your reaction time and the distance traveled while braking.
1. Distance traveled during reaction time:
Your reaction time is given as 6.904 m/s. This represents the distance you travel before you are able to react and hit the brakes. To calculate the distance traveled during this time, you simply multiply your reaction time by your initial velocity:
Distance = Reaction Time × Initial Velocity
Distance = 6.904 m/s × 30 m/s
2. Distance traveled while braking:
If we assume that you brake with maximum efficiency and bring the car to a stop in the minimum possible distance, the distance traveled while braking can be calculated using the braking distance formula:
Distance = (Initial Velocity squared) / (2 × Deceleration)
The deceleration can be calculated using the equation:
Deceleration = (Final Velocity squared - Initial Velocity squared) / (2 × Distance)
Given that your initial velocity is 30 m/s and your final velocity is 0 m/s (since you come to a stop), we can substitute these values into the deceleration equation:
Deceleration = (0 m/s - 30 m/s)² / (2 × Distance)
Deceleration = (-30 m/s)² / (2 × Distance)
Now, to find the distance traveled while braking, we need to equate the distance traveled during the braking phase to the distance traveled during your reaction time:
Distance = Distance traveled during reaction time + Distance traveled while braking
By substituting the formulas we derived earlier, we can solve for the distance traveled while braking:
6.904 m/s × 30 m/s = (-30 m/s)² / (2 × Distance) + Distance
Now we can solve this equation to find the distance traveled while braking.