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M9.4MechanicsStretch

Constant Acceleration Formulae 2

This lesson completes the SUVAT set with the three remaining equations, including the one with no time and the two displacement formulas. With all five you can solve any constant-acceleration problem.

30 min Constant Acceleration
Edexcel AS Level Maths: 9.4 Constant Acceleration Formulae 2Curated by Kepler, not produced by us. Watch it before the notes below.
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What you'll be able to do

  • Use s = ut + ½at²
  • Use v² = u² + 2as
  • Use s = vt − ½at²
  • Choose the most efficient SUVAT equation
1

The remaining equations

Two displacement equations and the “no-time” equation complete the set. The v2=u2+2asv^2 = u^2 + 2as form is especially useful when time is neither known nor wanted.

s=ut+12at2s = ut + \tfrac{1}{2}at^{2}
No vv.
v2=u2+2asv^{2} = u^{2} + 2as
No tt.
s=vt−12at2s = vt - \tfrac{1}{2}at^{2}
No uu.
2

Worked example

Identify the four relevant quantities, then substitute carefully — watching signs, especially for deceleration (negative aa).

Example 1A car decelerates from 20 m/s at 4 m/s² until it stops. Find the distance.
1Knowns: u=20u = 20, v=0v = 0, a=−4a = -4; want ss (no tt).
2Use v2=u2+2asv^2 = u^2 + 2as: 0=400+2(−4)s0 = 400 + 2(-4)s.
38s=4008s = 400.
Answers=50s = 50 m

Tip — No time involved (or wanted)? Reach for v² = u² + 2as.

3

Choosing efficiently

All five SUVAT equations are on the formula sheet for mechanics, but choosing the one that avoids an extra step saves time. Match the equation to the four quantities in play.

Formula recap

s=ut+12at2s = ut + \tfrac{1}{2}at^{2}
Displacement (no v).
v2=u2+2asv^{2} = u^{2} + 2as
No time.
s=vt−12at2s = vt - \tfrac{1}{2}at^{2}
Displacement (no u).

Common mistakes to avoid

Using a positive a for deceleration.
Deceleration is negative acceleration — use a negative value.
Choosing an equation with the unknown you do not want.
Pick the equation that includes your three knowns and the target unknown only.

Key takeaways

  • Remaining SUVAT: s = ut + ½at², v² = u² + 2as, s = vt − ½at².
  • Use v² = u² + 2as when time is not involved.
  • Watch signs: deceleration means negative a.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.