Assuming that it takes 0.10 s for the driver to react before applying the brakes, what is the stopping distance (the distance from the point where the driver first sees the need to stop to the point where the car comes to a stop) for a car traveling at 25 m/s if the deceleration due to the brakes is 3.5 m/s2?
vf^2=vi^2+2ad
solve for d. Now, add that to the distance in reaction time, 25*.1 meters
92m
21?
To find the stopping distance, we need to consider two things: the time taken for the driver to react and the time taken for the car to actually stop.
Step 1: Calculate the time taken for the driver to react.
Given that it takes 0.10 seconds for the driver to react, we can assume the initial speed remains constant during this time. Therefore:
Time taken for reaction = 0.10 seconds.
Step 2: Calculate the distance covered during the reaction time.
To find the distance covered during the reaction time, we use the equation:
Distance = Speed × Time
Given that the initial speed is 25 m/s and the reaction time is 0.10 seconds, we can calculate the distance covered during this time:
Distance covered during reaction time = 25 m/s × 0.10 s
Step 3: Calculate the time taken to stop the car.
To find the time taken to stop the car, we use the equation:
Time = Speed / Acceleration
Given that the speed is 25 m/s and the deceleration is 3.5 m/s², we can calculate the time taken to stop the car:
Time taken to stop = 25 m/s / 3.5 m/s²
Step 4: Calculate the distance traveled during the deceleration.
To find the distance traveled during the deceleration, we use the equation:
Distance = (Initial Speed × Time) + (0.5 × Acceleration × Time²)
Given that the initial speed is 25 m/s, the deceleration is 3.5 m/s², and the time taken to stop is calculated in Step 3, we can find the distance traveled during the deceleration.
Step 5: Calculate the total stopping distance.
The stopping distance is the sum of the distance covered during the reaction time (Step 2) and the distance traveled during the deceleration (Step 4).
By following these steps and performing the calculations, we can find the stopping distance for the car traveling at 25 m/s with a reaction time of 0.10 seconds and a deceleration of 3.5 m/s².