A car is initially travelling at a constant speed of 20 m/s along a highway. Suddenly, the driver applies the brakes, causing the car to accelerate at -5.0 m/s^2. If the driver applied the brakes 0.50s late, determine the distance the car travels from the moment the driver is about to brake until it stops.
Determine the two distances, and add them up.
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no
To determine the distance the car travels from the moment the driver is about to brake until it stops, we need to break the problem down into two parts: the distance traveled during the initial constant speed and the distance traveled while decelerating.
1. Distance traveled during the initial speed:
When the driver is about to brake, the car is already traveling at a constant speed of 20 m/s. To calculate the distance traveled during this time, we use the formula:
Distance = (initial speed) x (time)
Given that the initial speed is 20 m/s and the time is 0.50 s, we can calculate the distance as:
Distance1 = 20 m/s x 0.50 s
Distance1 = 10 meters
So, the car travels 10 meters during the initial speed.
2. Distance traveled while decelerating:
Now, we need to calculate the distance traveled while the car decelerates. We can use the equation of motion:
Distance = (initial velocity) x (time) + (1/2) x (acceleration) x (time)^2
Since the car is decelerating, the acceleration has a negative value (-5.0 m/s^2). The initial velocity is the speed of the car just before braking (20 m/s), and the time is the difference between the time of braking and the initial speed time (0.50 s).
Distance2 = (20 m/s) x (0.50 s) + (1/2) x (-5.0 m/s^2) x (0.50 s)^2
Distance2 = 10 meters - 0.625 meters
Distance2 = 9.375 meters
Therefore, the car travels 9.375 meters while decelerating.
To find the total distance traveled, we add the distance traveled during the initial speed to the distance traveled while decelerating:
Total distance = Distance1 + Distance2
Total distance = 10 meters + 9.375 meters
Total distance = 19.375 meters
So, the distance the car will travel from the moment the driver is about to brake until it stops is approximately 19.375 meters.