Three Golden Equations

Why it matters

Double your driving speed and your braking distance doesn't double — it QUADRUPLES. Three little equations know this, and every driving school in the world teaches their consequence.

The idea in plain words

The three equations of uniformly accelerated motion. Tap them.

v = u + at · s = ut + ½at² · v² = u² + 2as

u = 20 m/s, brakes give a = −4 m/s². Stopping distance?

50 m

• equation 1: v = u + at — no s — connects speeds and time
• equation 2: s = ut + ½at² — no v — position from time
• equation 3: v² = u² + 2as — no t — the braking-distance equation
• the trap: signs — deceleration enters as NEGATIVE a — forget the minus, fail the numerical
• 0 = u² + 2as → s = u²/2|a| = 400 ÷ 8

Predict first

A car's braking distance at 20 m/s is 50 m. At 40 m/s (same brakes) it is…

v² = u² − 2as with v = 0 gives s = u²/2a. Square the speed ratio: 2² = 4× the distance. Speed kills quadratically.

• 200 m — braking distance goes as u² — correct
• 100 m — double speed, double distance
• 50 m — brakes are brakes

What you do

Read u and the braking a, CALL the stopping distance, then hit the brakes and face the physics.

Check yourself

Which equation needs NO time?

Pick the equation missing the quantity you neither have nor want — that's the entire strategy.

From rest with a = 2 m/s², distance in 5 s is…

s = 0 + ½ × 2 × 25 = 25 m.

These three equations are valid only when…

They're derived for uniform acceleration — free fall qualifies, a car in traffic does not.

• v² = u² + 2as — correct
• v = u + at
• s = ut + ½at²
• 25 m — correct
• 10 m
• 50 m
• acceleration is CONSTANT — correct
• motion is circular
• always, for any motion