Determine how long it will take given the scenario below (in time and in distance) to react to the car in front of you. Assume that the car in front of you takes 3 seconds to change speeds.
Reaction time 1.6 seconds
Speed: 75 mph
Initial velocity: 33.53
Final velocity: 29.06
Mass of car: 1500 kg
Effective force of brakes: 14400.00N
To determine how long it will take to react to the car in front of you, we need to calculate the distance it travels during your reaction time. Then, we can calculate the time it takes to bring your car to a stop after reacting.
First, let's calculate the distance the car in front of you travels during your reaction time.
1. Convert the speed from miles per hour to meters per second:
Speed = 75 mph = (75 * 1609.34 m) / (1 h * 3600 s) = 33.528 m/s
2. Calculate the distance traveled during reaction time:
Distance = Speed * Reaction time = 33.528 m/s * 1.6 s = 53.645 meters
Now, let's calculate the time it takes to bring your car to a stop after reacting.
3. Calculate the change in velocity:
Change in velocity = Final velocity - Initial velocity = 29.06 m/s - 33.53 m/s = -4.47 m/s (negative since the car is slowing down)
4. Calculate the acceleration using Newton's second law of motion:
Acceleration = Force / Mass = 14400 N / 1500 kg = 9.6 m/s^2
5. Calculate the time taken to stop the car using the formula:
Time = (Change in velocity) / (Acceleration) = (-4.47 m/s) / (9.6 m/s^2) = -0.4655 s
Note: The negative sign indicates that the car is decelerating.
Finally, to determine the total time it will take to react and stop the car, we add the reaction time to the stopping time:
Total time = Reaction time + Stopping time = 1.6 s + (-0.4655 s) = 1.1345 seconds
Therefore, it will take approximately 1.1345 seconds for you to react and bring your car to a stop after the car in front of you changes speeds. The distance traveled during this time will be approximately 53.645 meters.