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import math
[docs]def time_to_cover(dist: float, speed: float, acc: float = 0.0) -> float:
"""
Returns the time for a moving object traveling at
speed and accelerating at acc to cover distance dist.
Assumes that all units are consistent (for example,
if distance is in meters, speed is in m/s).
The returned value will be non-negative
(but may be math.inf under some circumstances).
"""
if dist == 0:
return 0
if abs(acc) < 1e-9:
if speed == 0:
return math.inf
t = dist / speed
return t if t >= 0 else math.inf
discriminant = speed**2 + 2 * acc * dist
if discriminant < 0:
return math.inf
rad = math.sqrt(discriminant)
t1 = (rad - speed) / acc
t2 = -(rad + speed) / acc
mnt = min(t1, t2)
if mnt >= 0:
return mnt
mxt = max(t1, t2)
if mxt >= 0:
return mxt
return math.inf
[docs]def distance_covered(time: float, speed: float, acc: float = 0.0) -> float:
"""
Returns the amount of distance covered by an object
moving at speed and accelerating with acc.
Assumes that all units are consistent (for example,
if distance is in meters, speed is in m/s).
"""
return time * (speed + 0.5 * acc * time)
[docs]def stopping_time(start_speed: float, deceleration: float) -> float:
"""
Returns the time it would take to stop from initial speed start_speed
by decelerating at a constant rate of deceleration.
Note that deceleration should be a non-negative value (not a negative acceleration).
"""
assert deceleration >= 0.0
if deceleration == 0.0:
return math.inf
return start_speed / deceleration
[docs]def stopping_distance(start_speed: float, deceleration: float) -> float:
"""
Returns the distance it would take to stop from initial speed start_speed
by decelerating at a constant rate of deceleration.
Note that deceleration should be a non-negative value (not a negative acceleration).
"""
assert deceleration >= 0.0
return 0.5 * start_speed * stopping_time(start_speed, deceleration)