The driver of the car traveling at a constant 25m/s sees a child suddenly run into the road. It takes the driver 0.45s to hit the brakes. As it slows, the car has a steady acceleration of 8.5m/s©ü. What the total distance the car move before it stops.
Before hitting the brakes, the car travels 0.45 s * 25 m/s = 11.25 m
While decelerating, it travels for
t = 25/8.5 = 2.94 seconds. During that time it travels 12.5 m/s*2.94s = 36.8 m
Add the two distances
To find the total distance the car moves before it stops, we need to consider two parts: the distance traveled during the driver's reaction time and the distance traveled while the car is decelerating.
1. Distance traveled during the driver's reaction time:
During the reaction time, the car is moving at a constant velocity of 25 m/s. Since distance (d) is equal to velocity (v) multiplied by time (t), we can calculate the distance traveled during the reaction time using the formula: d = v * t.
d = 25 m/s * 0.45 s
d = 11.25 m
Therefore, during the driver's reaction time, the car travels a distance of 11.25 meters.
2. Distance traveled while decelerating:
The car experiences a constant acceleration of -8.5 m/s² (negative because it's decelerating). We need to find the distance traveled during this deceleration phase.
We can use the kinematic equation:
v² = u² + 2as
Where:
v = final velocity (0 m/s, since the car comes to a stop),
u = initial velocity (25 m/s),
a = acceleration (-8.5 m/s²),
s = distance traveled.
Rearranging the equation to solve for distance (s), we have:
s = (v² - u²) / (2a)
s = (0² - 25²) / (2 * -8.5)
s = (-625) / (-17)
s ≈ 36.76 m
Therefore, the distance traveled while decelerating is approximately 36.76 meters.
Total distance traveled = distance during reaction time + distance while decelerating
Total distance traveled = 11.25 m + 36.76 m
Total distance traveled ≈ 48.01 m
Hence, the total distance the car moves before it stops is approximately 48.01 meters.