When you try to stop your car in an emergency, there is some time before you can react.Your car is going 25 m/s and your reaction time is 0.20 s, then after you hit your brakes it decelerates at 9.5 m/s2. How far will your car travel before it stops?
as in your Anonymous post,
It takes t = 25/9.5 seconds to stop once the brakes are applied.
s = 25*0.2 + 25t - 4.75 t^2 is the total stopping distance
To calculate the distance your car will travel before it stops, we need to consider two parts: the distance covered during your reaction time and the distance covered while decelerating.
1. Distance covered during the reaction time:
Given that your car is moving at a speed of 25 m/s and your reaction time is 0.20 s, you can calculate the distance covered before you react by multiplying the speed by the reaction time:
Distance = Speed × Time
Distance = 25 m/s × 0.20 s
Distance = 5 meters
2. Distance covered while decelerating:
To find the distance covered while decelerating, we need to use the formula:
Distance = (Initial Speed × Time) + (0.5 × Deceleration × Time^2)
In this case:
Initial Speed = 25 m/s (car's speed)
Deceleration = -9.5 m/s^2 (negative sign indicates deceleration)
Time = Reaction Time + Time to Stop
Time to Stop is the time it takes for the car to come to a stop once the brakes are applied.
Since we want to find the total distance, we need to find the time it takes for the car to come to a stop:
Using the formula: Time to Stop = Final Speed / Deceleration
Final Speed is 0 m/s since the car comes to a stop.
Time to Stop = 0 m/s / (-9.5 m/s^2)
Time to Stop = 0 s (The time taken to stop is 0 seconds since the final speed is 0 m/s)
Therefore:
Total Time = Reaction Time + Time to Stop
Total Time = 0.20 s + 0 s
Total Time = 0.20 s
Now we can calculate the distance covered while decelerating:
Distance = (Initial Speed × Time) + (0.5 × Deceleration × Time^2)
Distance = (25 m/s × 0.20 s) + (0.5 × (-9.5 m/s^2) × (0.20 s)^2)
Distance = 5 m + (-0.190 m)
Distance = 4.81 m
So, the total distance your car will travel before it stops is approximately 5 meters (due to reaction time) + 4.81 meters (due to deceleration) = 9.81 meters.