A car is traveling 15 m/s when the driver sees a child standing on the road. He takes 0.8 s to react, then steps on the brakes and slows at 8.0 m/s2. How far does the car go before it stops?
To find the distance the car travels before it stops, we need to calculate the distance covered during the driver's reaction time and the distance covered during the braking period.
1. Distance covered during the driver's reaction time:
During the driver's reaction time, the car is still moving at its initial speed of 15 m/s. The formula to calculate the distance covered during this time is:
Distance = Speed * Time
Given that the driver's reaction time is 0.8 s, and the car's initial speed is 15 m/s:
Distance = 15 m/s * 0.8 s
Distance = 12 meters
So, during the reaction time, the car covers a distance of 12 meters.
2. Distance covered during the braking period:
To calculate the distance covered during the braking period, we need to first calculate the time it takes for the car to stop. We can use the formula:
Time = Change in Speed / Acceleration
Given that the car slows down at an acceleration of 8.0 m/s² and the final speed is 0 m/s:
Time = (0 m/s - 15 m/s) / (-8.0 m/s²)
Time = -15 m/s / -8.0 m/s²
Time = 1.875 s
Now we can calculate the distance covered during the braking period using the formula:
Distance = Initial Speed * Time + 0.5 * Acceleration * Time²
Given that the initial speed is 15 m/s, the time taken is 1.875 s, and the acceleration is -8.0 m/s²:
Distance = 15 m/s * 1.875 s + 0.5 * (-8.0 m/s²) * (1.875 s)²
Distance = 28.125 m + 0.5 * (-8.0 m/s²) * 3.5156 s²
Distance = 28.125 m - 0.5 * 8.0 m/s² * 12.351
Distance = 28.125 m - 39.216 m
Distance = -11.091 m
The negative sign indicates that the car could not come to a complete stop within the given distance.
Therefore, to sum up, the car travels 12 meters during the driver's reaction time and -11.091 meters during the braking period before coming to a stop.
To find the distance the car will travel before it stops, we need to break down the problem into several steps:
Step 1: Calculate the distance traveled during the driver's reaction time.
During the driver's reaction time of 0.8 s, the car continues moving at a constant velocity of 15 m/s. To find the distance traveled, we multiply the velocity by the time:
Distance = Velocity × Time = 15 m/s × 0.8 s = 12 meters
Step 2: Calculate the distance traveled while the car is decelerating.
Once the driver reacts to the child on the road, the car starts decelerating at a rate of 8.0 m/s^2 until it stops. To find the distance traveled while decelerating, we can use the following equation of motion:
Distance = (Velocity^2 - Initial Velocity^2) / (2 × Acceleration)
In this case, the initial velocity is 15 m/s, the final velocity is 0 m/s since the car stops, and the acceleration is -8.0 m/s^2 (negative sign due to deceleration):
Distance = (0^2 - 15^2) / (2 × -8.0) = (-225) / (-16) ≈ 14.06 meters
Step 3: Calculate the total distance traveled.
To get the total distance traveled by the car before it stops, we need to sum up the distances calculated in Step 1 and Step 2:
Total Distance = Distance during reaction time + Distance while decelerating
Total Distance = 12 meters + 14.06 meters ≈ 26.06 meters
Therefore, the car will go approximately 26.06 meters before coming to a stop.
d = Vo*t + (V^2-Vo^2)/2a.
d = 15m/s*0.8s + (0-225)/16 = 26.1 m.