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 Video by Zeeshan Zamurred Constant Acceleration

Edexcel AS Level Maths: 9.4 Constant Acceleration Formulae 2Watch the full walkthrough 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

The remaining equations

Two displacement equations and the “no-time” equation complete the set. The $v^{2} = u^{2} + 2 a s$ form is especially useful when time is neither known nor wanted.

s = u t + \frac{1}{2} a t^{2}

v

v^{2} = u^{2} + 2 a s

t

s = v t - \frac{1}{2} a t^{2}

u

Worked example

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

1Knowns:

u = 20

v = 0

a = - 4

; want

s

(no

t

2Use

v^{2} = u^{2} + 2 a s

0 = 400 + 2 (- 4) s

8 s = 400

Answer

s = 50

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

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 = u t + \frac{1}{2} a t^{2}

Displacement (no v).

v^{2} = u^{2} + 2 a s

No time.

s = v t - \frac{1}{2} a t^{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.

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