Free Fall

Free Fall Motion

Free fall is motion under gravity alone when air resistance is ignored. Near Earth's surface every object falls with the same acceleration of about 9.8 m/s², so speed grows by 9.8 m/s every second. Speed is v = gt and distance is h = ½gt², and the slope of a velocity-time graph is the gravitational acceleration g. On this page, change the time to watch the falling ball and the v-t graph update together.

What is Free Fall?

🍎 Intuition — A Falling Apple

①Without air resistance, a feather and a ball fall together

②Gravity pulls objects down

③Free fall: motion under gravity only

Time1.5s

Speed Keeps Increasing

📈 Constant Acceleration

①Free fall adds 9.8 m/s every second

②1 s: 9.8 m/s, 2 s: 19.6 m/s, 3 s: 29.4 m/s

③This kind of motion is called 'constant-acceleration motion'

Gravitational Acceleration g

🌍 g = 9.8 m/s²

①On Earth all objects fall with the same acceleration

②Called g, about 9.8 m/s²

③In a v-t graph, slope = acceleration = g

④Triangle area = distance

Gravitational Acceleration

g ≈ 9.8 m/s²

Earth's surface gravity

Summary

Free-Fall Velocity

v = gt

Speed = g × time

Free-Fall Distance

h = 12gt²

Distance = ½ × g × time²

Speed–Distance Relation

v² = 2gh

Use when time is not given

🎯 Exam Points

①Free fall = under gravity only (no air resistance)

②g ≈ 9.8 m/s² (constant)

③v = gt → speed proportional to time

④h = ½gt² → distance proportional to time²

⑤v-t graph: line through origin, slope = g

Examples and Unit Test

Example 1

A ball is released and falls freely. Taking the gravitational acceleration as g = 9.8 m/s², what is the ball's velocity 3 seconds later in m/s? (ignore air resistance)

In free fall, velocity v = g × t.

v = 9.8 m/s² × 3 s = 29.4 m/s.

▸ 29.4 m/s (9.8 × 3)

Free-fall velocity is proportional to time, rising by 9.8 m/s every second.

Example 2

When the same ball is released, how far does it fall in 2 seconds, in metres? (g = 9.8 m/s², ignore air resistance)

The free-fall distance is h = ½ × g × t².

h = ½ × 9.8 × 2² = ½ × 9.8 × 4 = 19.6 m.

▸ 19.6 m (½ × 9.8 × 2² = 19.6)

The fall distance is proportional to the square of time, so it grows faster as time goes on.

Unit Test

Which statement about free-fall motion is correct?

①A heavy object always falls before a light one (ignoring air resistance)

②The velocity-time graph of free fall is a straight line through the origin

③Free fall is uniform motion at constant velocity

④The gravitational acceleration g grows with the mass of the object

⑤The fall distance is directly proportional to time

▸ ② The velocity-time graph of free fall is a straight line through the origin

Ignoring air resistance, objects fall together regardless of weight (① wrong), and free fall is uniformly accelerated motion with increasing velocity (③ wrong).

The gravitational acceleration g is constant regardless of mass (④ wrong), and the fall distance is proportional to the square of time (⑤ wrong); the v-t graph is a straight line through the origin with slope g (② correct).

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