A car is traveling 26 m/s when the driver sees a child standing in the road. He takes 0.8 s to react, then steps on the brakes and slows at 6.0 m/s2. How far does the car go before it stops?
In .8 seconds he goes 26 * .8 meters
then the problem is acceleration with initial speed Vo = 26 and acceleration = -6 m/s^2
time to deacceletate to 0:
v = Vo + a t
0 = 26 - 6 t
t = 26/6
distance = .8* 26 + 26 t - (1/2) 6 * t^2
The distance travelled during the "reaction time" t1 is
X1 = V*t1 = 26 m/s * 0.8 s. = ?
The time required to decelerate to 0 is t2 = V/a = 4.33 s
The distance travelled while decelerating is the average velocity multipled by t2.
X2 = (V/2)(V/a) = V^2/(2a) = ?
Add X1 and X2 for the answer.
Ah, good. I am off for a while :)
To find the distance the car travels before it stops, we need to consider two phases: the reaction time and the braking time.
First, let's calculate the distance the car travels during the reaction time. The car is initially traveling at a constant velocity of 26 m/s, so in 0.8 seconds, the car will travel:
Distance during reaction time = 26 m/s * 0.8 s = 20.8 meters
Next, let's calculate the distance the car travels during the braking time. The car is slowing down at a rate of 6.0 m/s^2 until it comes to a stop. We can use the following equation to calculate the distance:
Distance during braking time = (initial velocity^2 - final velocity^2) / (2 * acceleration)
The initial velocity is 26 m/s, the final velocity is 0 m/s since the car comes to a stop, and the acceleration is -6.0 m/s^2 (negative because the car is slowing down). Plugging in the values:
Distance during braking time = (26 m/s)^2 - (0 m/s)^2 / (2 * -6.0 m/s^2)
= 676 m^2/s^2 / -12 m/s^2
= -56.33 meters (rounded to two decimal places)
Since distance cannot be negative, we ignore the negative sign and take the absolute value:
Distance during braking time = 56.33 meters
Finally, we add the distances from the reaction time and the braking time to get the total distance traveled:
Total distance = Distance during reaction time + Distance during braking time
= 20.8 meters + 56.33 meters
= 77.13 meters
Therefore, the car will travel a total distance of 77.13 meters before it stops.