A car is traveling 15 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?

44.6

To find the distance the car travels before it stops, we can break down the problem into three components: the distance traveled during the reaction time, the distance traveled during the deceleration, and the total distance traveled.

1. Distance traveled during the reaction time:
The driver's reaction time is given as 0.8 seconds. During this time, the car is still moving at a constant velocity of 15 m/s. The formula to calculate the distance traveled during this time is:

Distance = Velocity × Time

So, the distance traveled during the reaction time is:
Distance = 15 m/s × 0.8 s = 12 meters

2. Distance traveled during deceleration:
After the reaction time, the driver steps on the brakes, and the car begins to slow down with a deceleration of 7 m/s^2. To find the distance traveled during this time, we can use the following formula of motion:

Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time^2)

Since the car comes to a stop, the final velocity (Vf) is 0 m/s. We need to find the time it takes for the car to stop. The formula for finding time (t) is:

Final Velocity = Initial Velocity + (Acceleration × Time)
0 m/s = 15 m/s + (-7 m/s^2 × Time)

Simplifying the above equation, we get:
7 m/s × Time = 15 m/s
Time = 15 m/s ÷ 7 m/s
Time ≈ 2.14 s

Now, we can calculate the distance traveled during deceleration:
Distance = (15 m/s × 2.14 s) + (0.5 × -7 m/s^2 × (2.14 s)^2)
Distance ≈ 32 meters

3. Total distance traveled:
The total distance traveled is the sum of the distance during the reaction time and the distance during deceleration:

Total Distance = Reaction Time Distance + Deceleration Distance
Total Distance = 12 meters + 32 meters
Total Distance = 44 meters

Therefore, the car travels 44 meters before it stops.