When I was traveling at 18m/s with my bike I approach traffic lights when I was 30m far from them they turned red and it took me to recognize and react by applying breaks then I decelerated to 4.6m/s2. How will I go and in which side of the traffic lights?
I don't Know the answer!
What do you mean by
"took me to recognize"
"how will I go"
To determine how far you will go and which side of the traffic lights you will end up on, we can use the equations of motion.
First, let's find the time it takes for you to react and apply the brakes. We can use the equation:
vf = vi + at
Where:
- vf is the final velocity (4.6 m/s),
- vi is the initial velocity (18 m/s),
- a is the acceleration (-4.6 m/s^2), and
- t is the time it takes to decelerate.
By rearranging the equation, we get:
t = (vf - vi) / a
t = (4.6 m/s - 18 m/s) / (-4.6 m/s^2)
t = 13.4 m/s / 4.6 m/s^2
t ≈ 2.91 seconds (rounded to two decimal places)
So, it takes you approximately 2.91 seconds to react and apply the brakes after the traffic lights turn red.
Next, let's determine the distance traveled during this reaction time using the equation:
d = vit + (1/2)at^2
Where:
- d is the distance traveled during reaction time (unknown),
- vi is the initial velocity (18 m/s),
- t is the time (2.91 seconds), and
- a is acceleration (-4.6 m/s^2).
By substituting the known values into the equation, we have:
d = (18 m/s)(2.91 s) + (1/2)(-4.6 m/s^2)(2.91 s)^2
d ≈ 26.298 m (rounded to three decimal places)
Therefore, during the reaction time, you travel approximately 26.298 meters.
Now, let's find the distance covered while decelerating using the same equation:
d = vit + (1/2)at^2
Where:
- d is the distance traveled during deceleration (unknown),
- vi is the initial velocity (18 m/s),
- a is the deceleration (-4.6 m/s^2), and
- t is the time (2.91 seconds).
By substituting the values into the equation, we have:
d = (18 m/s)(2.91 s) + (1/2)(-4.6 m/s^2)(2.91 s)^2
d ≈ 37.984 m (rounded to three decimal places)
Therefore, during deceleration, you travel approximately 37.984 meters.
Adding the two distances together:
Total distance = 26.298 m + 37.984 m
Total distance ≈ 64.282 m (rounded to three decimal places)
So, you will travel approximately 64.282 meters before coming to a stop.
As for which side of the traffic lights you will be on, it depends on your position relative to the traffic lights when you start decelerating. We would need additional information, such as the distance between your initial position and the traffic lights, to determine which side you will end up on.