A car is traveling at 24.4 m/s. If the driver has a reaction time of 1 second, what will be his stopping distance if his car slows down at 8 m/s2?
d = Vo*t + (V^2-Vo^2)/2a
d = 24.4*1 + (0-24.4^2)/-16 = 61.6 m.
To find the stopping distance of a car, we need to consider two components: the distance covered during the driver's reaction time and the distance covered while the car is slowing down.
First, let's calculate the distance covered during the driver's reaction time. The car is traveling at a speed of 24.4 m/s, and the driver's reaction time is 1 second. During this time, the car will continue to move forward at its current speed. Therefore, the distance covered during the reaction time can be calculated using the formula:
Distance = Speed × Time
Distance = 24.4 m/s × 1 second = 24.4 meters
Next, let's calculate the distance covered while the car is slowing down. The car slows down at a rate of 8 m/s². To calculate the distance covered during deceleration, we need to use the formula:
Distance = (Speed² - Initial Speed²) / (2 × Acceleration)
Here, the initial speed is 24.4 m/s, the final speed is 0 (as the car comes to a stop), and the acceleration is -8 m/s² (negative because it is deceleration).
Distance = (0 - 24.4²) / (2 × -8)
Distance = (-595.36) / (-16)
Distance = 37.21 meters
Now, we can find the total stopping distance by adding the distance covered during the reaction time and the distance covered while slowing down:
Total Stopping Distance = Distance covered during reaction time + Distance covered during slowing down
Total Stopping Distance = 24.4 meters + 37.21 meters
Total Stopping Distance = 61.61 meters
Therefore, the car's stopping distance will be approximately 61.61 meters.
To find the stopping distance, we need to consider the reaction time and the deceleration of the car.
1. First, let's calculate the distance covered during the driver's reaction time.
Distance = Speed x Time
Distance = 24.4 m/s x 1 s
Distance = 24.4 m
2. Now, let's calculate the distance covered while decelerating.
The deceleration is -8 m/s^2 (negative sign because the car is slowing down).
Using the formula:
Velocity^2 = Initial velocity^2 + 2 * acceleration * distance
Rearranging the formula, we get:
Distance = (Velocity^2 - Initial velocity^2) / (2 * acceleration)
The initial velocity is 24.4 m/s and the final velocity is 0 m/s (since the car is stopping).
Distance = (0^2 - 24.4^2) / (2 * -8)
Distance = (-24.4^2) / (-16)
Distance = 376.96 / 16
Distance = 23.56 m
3. Finally, add the distance covered during the reaction time and the distance covered while decelerating.
Stopping distance = Distance covered during reaction time + Distance covered while decelerating
Stopping distance = 24.4 m + 23.56 m
Stopping distance = 47.96 m
Therefore, the stopping distance of the car will be approximately 47.96 meters.