a car is traveling 20.0 m/s when the driver sees a child standing in the road. he takes 0.80 seconds to react, then steps on the brakes and slows at -7.0 m/s squared. how far does the car go before it stops?

To find the distance the car goes before it stops, we can break down the problem into two parts: the reaction time and the braking distance.

1. Reaction time:
The initial velocity of the car is 20.0 m/s, and it takes the driver 0.80 seconds to react. During this time, the car will continue moving with its initial velocity.

The formula to calculate the distance covered during this time is:
Distance = Velocity × Time

Distance = 20.0 m/s × 0.80 s
Distance = 16.0 meters

So, during the reaction time, the car covers a distance of 16.0 meters.

2. Braking distance:
After the reaction time, the driver steps on the brakes and the car slows down at an acceleration of -7.0 m/s^2. We need to find the distance covered during this time until the car comes to a stop.

The formula to calculate the distance covered during uniform acceleration is:
Distance = (Final Velocity^2 - Initial Velocity^2) / (2 × Acceleration)

The final velocity will be 0 m/s (since it comes to a stop), and the initial velocity is 20.0 m/s. The acceleration is -7.0 m/s^2.

Distance = (0^2 - 20.0^2) / (2 × (-7.0))
Distance = (-400.0) / (-14.0)
Distance = 28.6 meters (approx.)

So, the car covers a distance of approximately 28.6 meters during the braking period.

To find the total distance traveled by the car, we add the distance covered during the reaction time and the braking distance:

Total distance = Reaction distance + Braking distance
Total distance = 16.0 meters + 28.6 meters
Total distance = 44.6 meters

Therefore, the car goes approximately 44.6 meters before it stops.

To find the distance the car goes before it stops, we need to consider two parts: the distance traveled during the driver's reaction time and the distance traveled while braking.

1. Distance during the driver's reaction time:
During the reaction time, the car maintains its initial velocity. The formula to calculate the distance during this time is:

Distance = Initial velocity * Time

Plugging in the values:
Initial velocity = 20.0 m/s
Time = 0.80 s

Distance = 20.0 m/s * 0.80 s = 16.0 meters

So, the car travels 16.0 meters during the driver's reaction time.

2. Distance while braking:
The car is decelerating at a rate of -7.0 m/s² (negative sign indicates deceleration). To find the distance traveled while braking, we can use the equation:

Distance = (Final velocity² - Initial velocity²) / (2 * Acceleration)

The initial velocity is 20.0 m/s, and the final velocity will be 0 m/s (since the car stops). The acceleration is -7.0 m/s².

Distance = (0 m/s)² - (20.0 m/s)² / (2 * -7.0 m/s²)
Distance = -400 m²/s² / -14 m/s²
Distance = 28.57 meters

Therefore, the car will travel approximately 28.57 meters while braking.

Now, to find the total distance, we sum up the distances during the reaction time and while braking:

Total distance = Distance during reaction time + Distance while braking
Total distance = 16.0 meters + 28.57 meters
Total distance = 44.57 meters

Therefore, the car will go approximately 44.57 meters before it stops.

d = Vo*t + (Vf^2-Vo^2)/2a.

d = 20*0.8 + 0-(20)^2 / -14 = 44.6 m.