Sure! Let's break down and solve the problem step-by-step.
### Problem Statement:
A driver is traveling at a speed of [tex]\( 18 \, \text{m/s} \)[/tex] and it takes them [tex]\( 0.7 \, \text{seconds} \)[/tex] to react when a dog walks into the road 40 meters ahead. We need to calculate the distance traveled by the car during the driver's reaction time.
### Given Data:
1. Speed of the car, [tex]\( v = 18 \, \text{m/s} \)[/tex]
2. Reaction time, [tex]\( t = 0.7 \, \text{seconds} \)[/tex]
3. Braking distance after reaction: 24 meters (not needed for this calculation)
4. Distance to the dog: 40 meters ahead (not needed for this calculation)
### Formula:
To find the distance traveled during the reaction time, we can use the formula:
[tex]\[ \text{distance} = \text{speed} \times \text{time} \][/tex]
### Step-by-Step Solution:
1. Identify the speed of the car ([tex]\( v \)[/tex]): The speed is given as [tex]\( 18 \, \text{m/s} \)[/tex].
2. Identify the reaction time ([tex]\( t \)[/tex]): The reaction time is given as [tex]\( 0.7 \, \text{seconds} \)[/tex].
3. Apply the formula for distance:
[tex]\[
\text{distance traveled} = v \times t
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
\text{distance traveled} = 18 \, \text{m/s} \times 0.7 \, \text{seconds}
\][/tex]
5. Calculate the distance:
[tex]\[
\text{distance traveled} = 12.6 \, \text{meters}
\][/tex]
### Conclusion:
The distance traveled by the car in the time it takes the driver to react is [tex]\( 12.6 \, \text{meters} \)[/tex].
