A car is traveling 28 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 7.0 m/s2. How far does the car go before it stops?
d1=Vo*t = 28m/s * 0.8s=22.4m to react.
d2 = (Vf^2 - Vo^2) / 2a,
d2 = (0 - (28)^2) / -14 = 56m,stopping
distance.
D = d1 + d2 = 22.4 + 56 = 78.4m before
stopping.
To calculate the distance the car goes before it stops, we need to consider two parts: the distance covered during the reaction time and the distance covered during the braking.
1. Distance covered during reaction time:
During the reaction time, the car continues to travel at a constant speed of 28 m/s. The formula to calculate the distance covered is:
Distance = Speed × Time
Given:
Speed = 28 m/s
Time = 0.8 s
Distance (reaction) = 28 m/s × 0.8 s
Distance (reaction) = 22.4 m
2. Distance covered during braking:
The car slows down to a stop, with an acceleration of 7.0 m/s^2. We can use the equation of motion to calculate the distance covered:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the car stops)
u = initial velocity (28 m/s)
a = acceleration (-7.0 m/s^2)
Rearranging the equation:
s = (v^2 - u^2) / 2a
Substituting the values:
s = (0^2 - (28 m/s)^2) / (2 × -7.0 m/s^2)
s = -784 m^2/s^2 / -14.0 m/s^2
s = 56 m
Therefore, the car goes 22.4 m during the reaction time and 56 m during the braking. The total distance covered before the car stops is:
Total distance = Distance (reaction) + Distance (braking)
Total distance = 22.4 m + 56 m
Total distance = 78.4 m
Therefore, the car goes 78.4 meters before it stops.
To find the distance the car goes before it stops, we can break down the problem into three steps:
1. Calculate the distance traveled during the driver's reaction time.
2. Calculate the distance traveled while decelerating.
3. Add the distances from step 1 and step 2 to find the total distance traveled.
Step 1: Calculate the distance traveled during the driver's reaction time.
We know that the car is traveling at a constant speed of 28 m/s for 0.8 s before the driver reacts. Therefore, during this time, the car will travel a distance equal to the product of the speed and the time:
Distance during reaction time = 28 m/s * 0.8 s
Step 2: Calculate the distance traveled while decelerating.
We're given that the car slows down at a rate of 7.0 m/s^2. To calculate the distance traveled while decelerating, we need to find the time it takes for the car to stop. We can use the formula:
Final velocity (Vf) = Initial velocity (Vi) + (acceleration * time)
Since we want to find the time it takes for the car to stop (Vf = 0), we can rearrange the formula:
0 = 28 m/s + (-7.0 m/s^2 * time)
Solving for time:
7.0 m/s^2 * time = 28 m/s
time = 28 m/s / 7.0 m/s^2
time = 4 s
Now that we know it takes 4 seconds for the car to stop, we can calculate the distance traveled during this time using the formula:
Distance while decelerating = Initial velocity * time + (1/2 * acceleration * time^2)
In this case, the initial velocity is 28 m/s, the time is 4 s, and the deceleration (acceleration) is -7.0 m/s^2 (negative because it's slowing down):
Distance while decelerating = 28 m/s * 4 s + (1/2 * -7.0 m/s^2 * (4 s)^2)
Step 3: Add the distances from step 1 and step 2 to find the total distance traveled.
Total distance traveled = Distance during reaction time + Distance while decelerating
Now you can substitute the values into the equation to find the answer.