Free Fall Motion and the Kinematic Equations
Everything you need to know about free fall using the kinematic equations. Learn how to solve problems for objects dropped, thrown upward, or thrown downward with clear explanations and solved examples.
Jump to a Section:
What is Free Fall?
Free fall is the motion of an object under the sole influence of gravity, with no other forces (like air resistance) acting on it.
In free fall near Earth’s surface, the acceleration is constant and equal to **g = 9.8 m/s²** downward. We usually take **a = –9.8 m/s²** when upward is positive.
Free fall problems are perfect applications of the kinematic equations because acceleration is constant.
Key Concepts & Sign Convention
Sign Convention (Recommended)
- Upward direction = Positive (+)
- Downward direction = Negative (–)
- Acceleration due to gravity a = **–9.8 m/s²**
Important Points
- At maximum height, vertical velocity v = 0
- Time to go up = time to come down (symmetric motion)
- Speed is same at same height (but direction opposite)
Kinematic Equations for Free Fall
1. v = v₀ – 9.8 t
2. Δy = (v + v₀)/2 × t
3. Δy = v₀ t – ½ × 9.8 t²
4. v² = v₀² – 2 × 9.8 × Δy
Replace a with –9.8 m/s² in the standard kinematic equations.
Solved Examples – Free Fall Motion
Example 1: Object Dropped
A stone is dropped from the top of a 120 m tall building. How long does it take to reach the ground and what is its impact speed?
Solution:
v₀ = 0, Δy = –120 m, a = –9.8 m/s²
Using Eq. 3: –120 = 0 – ½×9.8×t² → t ≈ 4.95 s
Using Eq. 1: v = 0 – 9.8×4.95 ≈ –48.5 m/s (48.5 m/s downward)
Example 2: Thrown Upward
A ball is thrown vertically upward at 25 m/s from ground level. Find maximum height and total time in air.
Maximum height (v = 0):
0 = 25² – 2×9.8×Δy → Δy = 31.9 m
Total time: Time up = 25/9.8 ≈ 2.55 s → Total time = 5.1 s
Example 3: Thrown Downward
A ball is thrown downward at 12 m/s from a 60 m bridge. Find impact speed and time to reach water.
Impact speed (Eq. 4):
v² = 12² + 2×9.8×60 → v ≈ 35.8 m/s downward
Time (Eq. 1): 35.8 = 12 + 9.8 t → t ≈ 2.43 s
Example 4: Same Height Different Direction
A ball is thrown upward at 15 m/s from a balcony. With what speed does it hit the ground 20 m below?
Using Eq. 4: v² = 15² + 2×9.8×20 → v ≈ 28.6 m/s downward
Problem-Solving Tips for Free Fall
- Always decide your positive direction before solving.
- Use Equation 4 when time is not given.
- At the highest point, vertical velocity is zero.
- For symmetric motion (thrown up and caught at same level), total time = 2 × (v₀/g).
- Speed is the same at the same height whether going up or down (direction differs).
Frequently Asked Questions
Is acceleration zero at the top of free fall?
No. Acceleration is always –9.8 m/s². Only velocity becomes zero at the highest point.
Does air resistance affect free fall problems?
In introductory physics, we usually ignore air resistance unless stated.
Can I use g = 10 m/s² instead of 9.8?
Yes, for simplicity in many exam problems, g = 10 m/s² is acceptable.
Continue Mastering Kinematics:
Free fall is one of the most common real-world applications of the kinematic equations. Practice these examples until you can solve any vertical motion problem quickly and confidently.
Last updated: April 2026 | Written for students by physics educators at physicalfundamentals.info