the car travels at 20m/s when the driver sees a child. It takes 0.8s to react, then steps on the brakes and slows at 7.0m/s^2. How far does the car go before it stops?
d = 20*0.8 + (Vf^2 _ Vo^2) / 2a,
d = 16 + (0 - (20)^2) / -14,
d = 16 + 28.57 = 44.57m.
To find the distance the car travels before stopping, we need to calculate the distance travelled during the reaction time and the distance travelled while braking.
1. Calculate the distance travelled during the reaction time:
The car travels at a constant speed of 20 m/s, and the reaction time is 0.8 seconds. So, during this time, the car travels a distance of:
Distance during reaction time = Speed * Time = 20 m/s * 0.8 s = 16 meters.
2. Calculate the distance travelled while braking:
To calculate the distance travelled while braking, we need to use the formula for distance with uniformly decelerated motion:
Distance = (Initial Velocity^2 - Final Velocity^2) / (2 * Acceleration)
In this case, the initial velocity is 20 m/s, the final velocity is 0 m/s (since the car stops), and the acceleration is -7.0 m/s^2 (negative because it is deceleration).
Plugging these values into the formula:
Distance = (20^2 - 0^2) / (2 * -7.0) = 400 / -14 = -28.57 meters
Since distance cannot be negative, we take the absolute value:
Distance = 28.57 meters
3. Calculate the total distance travelled:
The total distance traveled is the sum of the distance during the reaction time and the distance while braking:
Total Distance = Distance during reaction time + Distance while braking
Total Distance = 16 meters + 28.57 meters = 44.57 meters
Therefore, the car travels approximately 44.57 meters before coming to a complete stop.