A car is traveling 26 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?
(0.8 * 26) + [(26 / 7.0) * 13]
To find the distance the car travels before it stops, we need to consider two parts: the time it takes for the driver to react and the time it takes for the car to come to a complete stop.
First, let's calculate the distance covered during the driver's reaction time.
The car is initially traveling at a speed of 26 m/s. The time taken by the driver to react is 0.8 seconds. Therefore, the distance covered during the reaction time can be found using the formula:
Distance = Initial speed × Time
Distance = 26 m/s × 0.8 s = 20.8 meters
Now, let's calculate the distance covered by the car while it's slowing down.
The car is slowing down at a rate of 7.0 m/s^2. We need to find the time it takes for the car to come to a complete stop. This can be calculated using the formula:
Time = Change in speed / Acceleration
Here, the change in speed is equal to 26 m/s (initial speed) since the car comes to a stop.
Time = 26 m/s / 7.0 m/s^2 = 3.714 seconds (approx.)
Now, to find the distance covered during this time, we can use the equation of motion:
Distance = Initial speed × Time - 0.5 × Acceleration × Time^2
Distance = 26 m/s × 3.714 s - 0.5 × 7.0 m/s^2 × (3.714 s)^2
Distance = 96.564 - 60.514
Distance = 36.05 meters (approx.)
Finally, to find the total distance traveled before the car stops, we need to sum the distance covered during the reaction time and the distance covered while slowing down.
Total distance = Distance during reaction time + Distance while slowing down
Total distance = 20.8 m + 36.05 m
Total distance = 56.85 meters (approx.)
Therefore, the car will travel approximately 56.85 meters before it stops.