Assume you are driving a car at a constant speed of 75.0 km/h. Suddenly you see a deer standing on the highway and you must put on the brakes. Your reaction time (time elapsed between the moment you see the deer and your foot hitting the brakes) is 0.116 sec. The brakes provide an acceleration of -5.4 m/s2. Find the distance (in m) the car travels (at 75.0 km/h) during your reaction time. Calculate the total distance (in m) traveled by the car before stopping.
75 km/hr = 20.833 m/s
so, at 75km/hr, the car travels
20.833 * 0.116 m
Then, it takes 20.833/5.4 seconds to stop, and the distance traveled while braking is
20.833t - 2.7t^2
where t is the above stopping time.
To find the distance the car travels during your reaction time, we can use the formula:
distance = initial velocity * time
First, we need to convert the initial velocity from km/h to m/s. Since 1 km/h is equal to 0.2778 m/s, the initial velocity of 75.0 km/h is:
75.0 km/h * 0.2778 m/s = 20.83 m/s
Next, we'll plug in the values into the equation:
distance = 20.83 m/s * 0.116 sec
Calculating this, we get:
distance = 2.4168 m
Therefore, the car travels approximately 2.4168 meters during your reaction time.
To find the total distance traveled by the car before stopping, we need to calculate the distance it takes for the car to come to a stop. We can use the equation:
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
Since the car comes to a stop, the final velocity is 0 m/s. We can rearrange the equation to solve for distance:
distance = (final velocity^2 - initial velocity^2) / (2 * acceleration)
Plugging in the given values:
distance = (0 m/s^2 - 20.83 m/s)^2 / (2 * -5.4 m/s^2)
Calculating this, we get:
distance = 72.2648 m
Therefore, the total distance traveled by the car before stopping is approximately 72.2648 meters.
To find the distance the car travels during your reaction time, we need to convert the speed from km/h to m/s since the acceleration is given in m/s^2.
1. First, convert the speed from km/h to m/s:
Speed = 75.0 km/h = (75.0 * 1000) / 3600 m/s = 20.83 m/s (rounded to two decimal places)
2. Now, we can calculate the distance the car travels during your reaction time using the formula:
Distance = Initial Velocity * Time + 0.5 * Acceleration * Time^2
Distance = (20.83 m/s) * (0.116 sec) + 0.5 * (-5.4 m/s^2) * (0.116 sec)^2
= 2.42 m (rounded to two decimal places)
Therefore, the car travels approximately 2.42 meters during your reaction time.
To calculate the total distance traveled by the car before stopping, we need to find the distance it takes for the car to come to a complete stop after applying the brakes.
3. To find the time it takes for the car to stop, we can use the equation:
Final Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Distance
Since the final velocity is 0 (the car comes to a stop), we can rearrange the equation:
0 = (20.83 m/s)^2 + 2 * (-5.4 m/s^2) * Distance
Solving for Distance:
Distance = ((20.83 m/s)^2) / (2 * 5.4 m/s^2)
= 9.84 m (rounded to two decimal places)
Therefore, the car travels approximately 9.84 meters before coming to a stop.
Therefore, the total distance traveled by the car before stopping is the sum of the distance traveled during your reaction time and the distance traveled to come to a stop:
Total Distance = Distance during reaction time + Distance to come to a stop
= 2.42 m + 9.84 m
= 12.26 m (rounded to two decimal places)
So, the total distance traveled by the car before stopping is approximately 12.26 meters.