user: What is the estimated time until collision if my car is traveling at a velocity of 20 m/s, accelerating at 2 m/s^2, and the vehicle ahead is moving at 15 m/s with an acceleration of 1 m/s^2, given that the initial distance between us is 50 meters?

Available functions:
name: get_headway
description: Calculates the headway, which is the distance from the front of the ego vehicle to the closest leading object, using curvilinear coordinates. This function requires the ego vehicle's information, the detected lane, and the 3D bounding boxes from perception data.
parameters: type: dict
required: ego_info
lane_info
bounding_boxes
properties: ego_info: type: dict
description: Information about the ego vehicle, including its position and orientation.
properties: position: type: dict
description: Curvilinear coordinates of the ego vehicle, consisting of lateral and longitudinal positions.
properties: lateral: type: float
description: Lateral position of the ego vehicle in meters.
longitudinal: type: float
description: Longitudinal position of the ego vehicle in meters.
orientation: type: float
description: Orientation of the ego vehicle in degrees.
lane_info: type: dict
description: Information about the detected lane.
properties: lane_id: type: string
description: Unique identifier for the detected lane.
lane_type: type: string
description: Type of the lane.
enum: regular
merge
exit
turn
bounding_boxes: type: array
items: type: dict
description: List of 3D bounding boxes representing detected objects. Each bounding box should include dimensions and the object's position relative to the ego vehicle.
name: get_time_headway
description: Calculates the time headway (THW), which is the time it will take for the ego vehicle to reach the closest leading object in curvilinear coordinates. Inputs include the ego vehicle's information, the detected lane, and the 3D bounding boxes of the perceived objects.
parameters: type: dict
required: ego_info
lane_info
bboxes
velocities
accelerations
properties: ego_info: type: dict
description: Contains the ego vehicle's current position and velocity.
properties: position: type: tuple
description: The vehicle's current position as a tuple of x, y, and z coordinates (meters).
items: type: float
velocity: type: float
description: The vehicle's current velocity in meters per second (m/s).
lane_info: type: dict
description: Information about the detected lane, including its curvature and width.
properties: curvature: type: float
description: The curvature of the lane at the ego vehicle's position (1/meters).
width: type: float
description: The width of the lane in meters (m).
bboxes: type: array
items: type: dict
description: List of 3D bounding boxes representing perceived objects. Each bounding box is described by its position and size.
velocities: type: array
items: type: float
description: List of velocities of the detected objects in meters per second (m/s).
accelerations: type: array
items: type: float
description: List of accelerations of the detected objects in meters per second squared (m/s^2).
name: get_time_to_collision
description: Calculates the time it will take for the ego vehicle to collide with the closest leading object in curvilinear coordinates, considering both vehicles' velocities and the leading object's acceleration.
parameters: type: dict
required: ego_velocity
ego_acceleration
leading_object_velocity
leading_object_acceleration
initial_distance
properties: ego_velocity: type: float
description: The current velocity of the ego vehicle in meters per second.
ego_acceleration: type: float
description: The current acceleration of the ego vehicle in meters per second squared.
leading_object_velocity: type: float
description: The current velocity of the leading object in meters per second.
leading_object_acceleration: type: float
description: The current acceleration of the leading object in meters per second squared.
initial_distance: type: float
description: The initial distance between the ego vehicle and the leading object in meters.