u · v · a · t · s · equations of motion · straight-line kinematics
A bike rolls faster when you push, a ball gains speed as it falls, a car slows as you brake. When acceleration is constant, four numbers — u, v, a, t — and the distance s are tied by a few famous equations. Dial them in the Motion Studio and watch a cart obey v = u + at and s = ut + ½at².
This page covers the SUVAT family: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u+v)t, for motion in a straight line with constant acceleration. By the end you'll be able to:
Cars, drops, trains and projectiles (the straight stretches) all lean on these equations — and "equations of motion" / kinematics is a core Class 9 chapter everywhere. We go beyond the syllabus, but we never skip it:
Searched as: equations of motion, v = u + at, s = ut + 1/2 at^2, v^2 = u^2 + 2as, constant acceleration, free fall.
Set u (start speed), a (acceleration) and watch to time t. The cart races along the track; readouts obey v = u + at and s = ut + ½at². Switch to the v–t tab — slope is a, area under the line is s. 🟢 real kinematics engine
Set u, a and t — watch the cart match v = u+at and s = ut+½at².
In plain terms: if acceleration stays constant, speed changes at a steady rate — and the distance you cover is what that changing speed adds up to.
u is how fast you start. a is how quickly speed changes each second. After time t, speed becomes v = u + at. Distance s is not just “speed × time” unless a = 0 — because the speed was changing while you moved.
s = ut + ½at² adds the extra push (or brake) into the distance. v² = u² + 2as lets you skip the clock. s = ½(u+v)t is average speed times time. Same physics; pick the form that fits the knowns.
The Track tab eases a cart along a ruler as time runs to your chosen t (motion-feel). The v–t tab draws a straight line from u to v — slope a, triangle/trapezoid area s. Presets: Drop (free fall), Cruise, Brake, Coast. 🟡 maths of the picture
Exams reward the method, not just the answer. Work it out one step at a time — read the thought, predict the line, then reveal it. Switch to practice to type your own numbers and check them.
Drag the numbers — watch v, s and the v–t idea update.
Some wrong ideas about sound and waves are so sticky they deserve their own warning label. Tap a card to bust the myth.
A guitar string's pitch is its vibration frequency. Shorten the string or tighten it and f rises, so λ in the air shortens while sound still cruises at ~340 m/s. Amplitude — how hard you pluck — sets loudness, not the note.
Ships and bats time echoes: d = vt/2 with v matched to water or air. Hospitals send MHz ultrasound into tissue; reflections map organs because soft and hard boundaries bounce waves differently.
Light reaches you almost instantly; thunder is sound at ~340 m/s. Counting seconds from flash to boom and dividing by three gives a rough distance in kilometres — a pocket wave-equation use outdoors.
Once humans could time, tune and reflect waves, they built concert halls, sonar, ultrasound machines and fibre that guides light.
Drag the ladder — everyday motions that obey constant-a models (approximately).
Scale changes; v = u + at stays the habit.
Physics you can hear. Each project below shows the wave idea you just met — and the measuring is what turns a demo into a science-fair winner.
Build: sprinkle dry rice on a drum skin or stretched balloon; tap beside it (not under the rice).
Measure: how far from the tap the rice still jumps — energy arrives without the skin sliding across.
Build: two paper cups, a taut string between the bases; whisper into one.
Measure: maximum clear distance, and what happens when the string goes slack (wave needs tension).
Build: clap toward a large wall; time the echo with a phone stopwatch (several trials).
Measure: average t, then d = 340t/2, and compare with a paced or mapped distance.
Build: stretch rubber bands of different lengths over a box; pluck and compare pitch.
Measure: length vs perceived pitch order — shorter or tighter → higher f.
Build: stretch a slinky on the floor; push one end forward sharply.
Measure: time for the pulse to reach the far end and estimate speed along the coils.
Build: use a free spectrum app to read the frequency of a tuning fork or tone generator.
Measure: f, assume v = 340 m/s, compute λ = v/f, and mark that length on the floor.
SUVAT looks like five letters until the first exam. Straight answers:
s displacement, u initial velocity, v final velocity, a acceleration, t time — the standard set for constant-acceleration motion in a straight line.
List knowns. If t is missing, try v² = u²+2as. If s is missing, try v = u+at. If a = 0, s = ut.
No — it is any change of velocity. Slowing down is acceleration with the opposite sign to your chosen positive direction.
Free-fall acceleration near Earth, about 9.8 m/s² (boards often use 10). Direction: toward Earth.
Not as the full story — circular motion needs centripetal ideas. Straight-line constant a is this chapter.
Spot these before the exam does.
Seven question formats, the way Beyond Dictionary serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000
Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.
A wave is energy on the move — the pond barely travels, yet the story of the pebble reaches every shore.