Drop a feather and a steel ball together in a tube with the air pumped out, and they hit the bottom side by side. Without air resistance objects fall the same way whatever their weight, and falling under gravity alone like this is called free fall.
An object in free fall gains about 9.8 m/s of speed every second. This constant acceleration is the acceleration due to gravity, g; the speed is v = gt and the distance fallen is h = ½gt².
Increasing the time in the first diagram, the marks the ball leaves every 0.5 s spread further and further apart; in the second graph the speed climbs as a straight line through the origin.
The slope of that line is g, and the area of the triangle under it is the distance fallen.
What Is Free Fall?
🍎 A Feather and a Steel Ball
①Without air resistance, a light feather and a heavy steel ball fall at the same time
②Objects fall because the Earth pulls on them: the force of gravity
③Falling under gravity alone, with no air resistance, is called free fall
④In real air, light, spread-out objects like feathers feel strong air resistance and fall slowly
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A ball released from rest in free fall, with its position every 0.5 s and its speed
1.5s
Speeding Up Steadily
📈 Uniform Acceleration
①An object in free fall gains about 9.8 m/s of speed every second
②After 1 s: 9.8 m/s; after 2 s: 19.6 m/s; after 3 s: 29.4 m/s
③Motion with constant acceleration like this is called uniformly accelerated motion
④The distance covered in each second keeps growing: 4.9 m in the first second, 14.7 m in the next
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Speed-time graph of free fall; the slope is the acceleration due to gravity and the area is the distance fallen
The Acceleration Due to Gravity, g
🌍 g ≈ 9.8 m/s²
①Near the Earth's surface all objects fall with the same acceleration
②This acceleration is called g and is about 9.8 m/s²
③On a speed-time graph, the slope of the line is the acceleration, g
④The area of the triangle under the line is the distance fallen
Acceleration due to gravity
g ≈ 9.8 m/s²
The acceleration due to gravity near the Earth's surface; on the Moon it is about 1.6 m/s²
Summary
Speed in free fall
v = gt
Speed = acceleration due to gravity × time
Distance in free fall
h = 12gt²
Distance fallen = ½ × acceleration due to gravity × time²
Speed and distance
v² = 2gh
Lets you find the speed from the height fallen, without knowing the time
🎯 Common Test Points
①Free fall: motion under gravity alone, ignoring air resistance
②The acceleration g ≈ 9.8 m/s² is constant
③v = gt: speed is proportional to time
④h = ½gt²: distance fallen is proportional to the square of time
⑤The speed-time graph is a straight line through the origin with slope g
Examples and Unit Review
Example 1
A ball is released from rest and falls freely. Taking g as 9.8 m/s², what is its speed after 3 seconds? (Ignore air resistance.)
1
In free fall the speed is v = g × t.
2
v = 9.8 m/s² × 3 s = 29.4 m/s.
▸ 29.4 m/s
In those same 3 seconds it falls ½ × 9.8 × 3² = 44.1 m, roughly the height of a 15-story building.
Example 2
How far does the same ball fall in 2 seconds after being released from rest? (g = 9.8 m/s², ignore air resistance)
1
The distance fallen is h = ½ × g × t².
2
h = ½ × 9.8 × 2² = ½ × 9.8 × 4 = 19.6 m.
▸ 19.6 m
Doubling the time makes the distance four times as large: 4.9 m in 1 s, 19.6 m in 2 s.
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
1
Ignoring air resistance, objects fall together regardless of weight (① wrong), and free fall is uniformly accelerated motion with increasing velocity (③ wrong).
2
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).