The driver of a car, traveling at a constant 25 m/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 8.5 m/s^2. What's the total distance the car moves before it stops?
distance=vi(t+.45)-1/2 a t^2
now, what is t?
vf=Vi-at solve for t, put it in the first equation.
So, 25(.45+.45)-1/2(8.5)(.45)^2?
yes, if you calculated time t right. I didn't check it.
To find the total distance the car moves before it stops, we need to calculate two distances: the distance traveled during the driver's reaction time and the distance traveled while decelerating.
1. First, let's calculate the distance traveled during the driver's reaction time.
The car is traveling at a constant speed of 25 m/s. In 0.45 seconds, the car will cover a distance equal to the product of its initial velocity and the reaction time:
Distance = Velocity × Time
Distance = 25 m/s × 0.45 s = 11.25 m
Therefore, during the driver's reaction time, the car will travel 11.25 meters.
2. Next, we need to determine the distance traveled while decelerating.
The car experiences a steady acceleration of -8.5 m/s^2. The negative sign indicates deceleration.
We can use the equation of motion to find the distance covered during deceleration:
Distance = (Final Velocity)^2 - (Initial Velocity)^2 / (2 × Acceleration)
The final velocity in this case is 0 m/s because the car comes to a stop. The initial velocity is 25 m/s, and the acceleration is -8.5 m/s^2.
Distance = (0 m/s)^2 - (25 m/s)^2 / (2 × -8.5 m/s^2)
Distance = 0 - 625 m^2/s^2 / (-17 m/s^2)
Distance = 625 m^2/s^2 / 17 m/s^2
Distance = (625/17) m^2/s^2 ≈ 36.76 m
Therefore, the distance traveled while decelerating is approximately 36.76 meters.
3. Finally, to find the total distance the car moves before it stops, we add the distance traveled during the reaction time to the distance traveled during deceleration:
Total Distance = Distance during reaction time + Distance during deceleration
Total Distance = 11.25 m + 36.76 m
Total Distance ≈ 48.01 m
Therefore, the total distance the car moves before it stops is approximately 48.01 meters.