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 Video by Zeeshan Zamurred Constant Acceleration

Edexcel AS Level Maths: 9.5 Vertical Motion Under GravityWatch the full walkthrough 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

Acceleration due to gravity

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

a = g \approx 9.8 m/s^{2} (downwards)

Free-fall acceleration (air resistance ignored).

Choosing a positive direction

Decide which direction is positive and apply it consistently. If $up$ is positive, then $g$ is $negative$ ( $- 9.8$ ), 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.

Up-and-down problems

For an object thrown up, at the highest point the velocity is momentarily $0$ (use this as a known $v$ ). The motion up and down is symmetric, and SUVAT handles the whole journey.

1At the top

v = 0

. Use

v = u + a t

0 = 14.7 - 9.8 t

Answer

t = 1.5

Formula recap

g \approx 9.8 m/s^{2}

Free-fall acceleration.

up positive \Rightarrow a = - 9.8

Sign convention.

v = 0 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.

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