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M9.5MechanicsStretch

Vertical Motion Under Gravity

An object in free fall has a constant downward acceleration g ≈ 9.8 m/s². That means the SUVAT equations apply directly to vertical motion — the only new skill is being consistent about the positive direction.

30 min Constant Acceleration
Edexcel AS Level Maths: 9.5 Vertical Motion Under GravityCurated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Use g ≈ 9.8 m/s² as the acceleration
  • Apply SUVAT to vertical motion
  • Choose and stick to a positive direction
  • Solve projectile-up-and-down problems
1

Acceleration due to gravity

Ignoring air resistance, every object near the Earth accelerates downward at g≈9.8g \approx 9.8 m/s². This constant acceleration means the SUVAT equations apply with a=ga = g.

a=g≈9.8 m/s2 (downwards)a = g \approx 9.8 \ \text{m/s}^2 \ (\text{downwards})
Free-fall acceleration (air resistance ignored).
2

Choosing a positive direction

Decide which direction is positive and apply it consistently. If up\textbf{up} is positive, then gg is negative\textbf{negative} (−9.8-9.8), and a downward initial velocity is also negative. Getting the signs consistent is the whole game.

Tip — Pick “up = positive”, then gravity is −9.8. Keep every quantity’s sign consistent with that choice.

3

Up-and-down problems

For an object thrown up, at the highest point the velocity is momentarily 00 (use this as a known vv). The motion up and down is symmetric, and SUVAT handles the whole journey.

Example 1A ball is thrown up at 14.7 m/s. How long to reach the top? (g = 9.8, up positive)
1At the top v=0v = 0. Use v=u+atv = u + at: 0=14.7−9.8t0 = 14.7 - 9.8t.
Answert=1.5t = 1.5 s

Formula recap

g≈9.8 m/s2g \approx 9.8 \ \text{m/s}^2
Free-fall acceleration.
up positive⇒a=−9.8\text{up positive} \Rightarrow a = -9.8
Sign convention.
v=0 at the highest pointv = 0 \ \text{at the highest point}
Key fact for thrown objects.

Common mistakes to avoid

Mixing signs — using +g while taking up as positive.
If up is positive, gravity acts downward, so a = −9.8.
Forgetting that v = 0 at the top of the flight.
At maximum height the velocity is momentarily zero.

Key takeaways

  • Free fall has constant acceleration g ≈ 9.8 m/s² downward.
  • SUVAT applies; choose a positive direction and keep signs consistent.
  • At the highest point of a throw, v = 0.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

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