4. When you try to stop your car in an emergency, there is some time before you can react. Your car is going 25 m/s and your reaction time is 0.20 s, then after you hit your brakes it decelerates at 9.5 m/s2. How far will your car travel before it stops?
To find the distance your car will travel before it stops, we need to consider the time it takes for you to react and the time it takes for the car to stop.
Let's break down the problem step by step:
1. First, we need to calculate the distance traveled during the reaction time. This can be done using the formula: distance = speed × time.
Given:
Initial speed of the car (v) = 25 m/s
Reaction time (t) = 0.20 s
Distance during the reaction time = 25 m/s × 0.20 s.
Plugging in the values, we get:
Distance during the reaction time = 5 m
2. Next, we need to calculate the distance traveled during the deceleration of the car. The formula for the distance traveled during deceleration is: distance = (final velocity^2 - initial velocity^2) / (2 × acceleration).
Given:
Initial speed of the car (v) = 25 m/s
Deceleration (a) = -9.5 m/s^2 (negative sign indicates deceleration)
Distance during deceleration = (0 m/s^2 - 25 m/s^2) / (2 × -9.5 m/s^2).
Simplifying the equation, we get:
Distance during deceleration = (-625 m^2/s^2) / (-19 m/s^2).
The negative signs cancel out, resulting in a positive value:
Distance during deceleration = 32.89 m.
3. Finally, we need to find the total distance traveled by summing up the distance during the reaction time and the distance during deceleration:
Total distance traveled = Distance during reaction time + Distance during deceleration.
Plugging in the values, we get:
Total distance traveled = 5 m + 32.89 m.
Therefore, the total distance your car will travel before it stops is approximately 37.89 meters.