Project: Distance fallen

Use this formula to find how far an object falls in a given time because of gravity:

d = (1/2)gt²

where d is the distance in meters, g is 9.8, and t is the time in seconds.

Write a function called distance_fallen that takes a time in seconds as an argument and returns the distance the object has fallen in that time. Here is how it could be used:

dist = distance_fallen(4.5)
print(dist)

Save the file as distance_fallen.py.

Show a solution

Try the project on your own first. This is one working solution, followed by its tests. Press Run to run the tests. Read them to see what thorough testing looks like, then change the solution and run again to watch a test fail.

def distance_fallen(time: float) -> float:
    """Return the distance in meters an object falls in `time` seconds."""
    gravity: float = 9.8
    return 0.5 * gravity * time * time

# ---- Tests ----
import sys
import unittest

class TestDistanceFallen(unittest.TestCase):
    def test_an_object_has_not_fallen_at_time_zero(self):
        self.assertEqual(distance_fallen(0), 0)

def test_one_second_of_falling_is_half_of_gravity(self):
        self.assertAlmostEqual(distance_fallen(1), 4.9)

def test_the_example_from_the_project(self):
        self.assertAlmostEqual(distance_fallen(4.5), 99.225)

def test_a_whole_number_of_seconds(self):
        self.assertAlmostEqual(distance_fallen(10), 490)

def test_doubling_the_time_quadruples_the_distance(self):
        self.assertAlmostEqual(distance_fallen(6), 4 * distance_fallen(3))

def test_a_fraction_of_a_second(self):
        self.assertAlmostEqual(distance_fallen(0.5), 1.225)

def test_a_negative_time_gives_the_same_distance_as_a_positive_one(self):
        self.assertAlmostEqual(distance_fallen(-2), distance_fallen(2))

# ---- Run the tests ----
loader = unittest.defaultTestLoader
suite = unittest.TestSuite(loader.loadTestsFromTestCase(case) for case in [TestDistanceFallen])
unittest.TextTestRunner(stream=sys.stdout, verbosity=2).run(suite)

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