Run three full laps of a circular track, and you’re back exactly where you started. Your distance is huge; your displacement is zero. This article covers kinematics.
✊ Must Know
Distance, Displacement, and Equations of Motion
- Distance vs. DisplacementDistance is the total path covered, a scalar. Displacement is the shortest straight-line change in position, a vector. They’re equal only for straight-line motion in one direction.
- Speed vs. VelocitySpeed is the rate of change of distance with time. Velocity is the rate of change of displacement with time.
- AccelerationAcceleration is the rate of change of velocity with time. It can be positive, negative, or zero.
- Equations of MotionThree equations connect velocity, acceleration, time, and distance for uniform acceleration: v = u + at, s = ut + ½at², and v² = u² + 2as.
- Free FallA body in free fall under gravity, ignoring air resistance, is a classic example of uniformly accelerated motion.
- The TrickRunning laps on a circular track shows the distinction sharply: complete whole laps and your displacement is zero, even though your distance covered keeps growing.
📘 Good to Know
Graphs and Free Fall
- Distance-Time GraphOn a distance-time graph, the slope represents speed. A straight line means constant speed; a curve means changing speed.
- Velocity-Time GraphOn a velocity-time graph, the area under the curve gives net displacement, not raw distance, since it’s a signed area that can add or cancel.
- Average SpeedAverage speed for a full trip is total distance divided by total time, not a simple average of two different speeds.
- Free Fall in a VacuumIn a vacuum, a coin, a feather, and a mango all fall at the same rate, since air resistance is what normally causes different fall speeds.
Naming the Type of Motion
- Rectilinear MotionRectilinear motion means moving along a straight line, as with a car on a straight road or a falling stone.
- Circular MotionCircular motion keeps an object at a constant distance from a fixed centre, as with a fan blade or a clock’s hands.
- Uniform Circular Motion Is AcceleratedMoving at constant speed around a circle still counts as accelerated motion, since the direction of velocity keeps changing even though its magnitude does not.
- Periodic MotionPeriodic motion repeats itself after a fixed interval of time, as with a swinging pendulum or a plucked guitar string.
- Combined MotionA rolling ball moves in a straight line while also rotating, combining rectilinear and circular motion at once.
Test Yourself
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🌟 Great to Know
Common Traps and Projectile Motion
- The Most Common TrapDistinguishing speed from velocity, and distance from displacement, is one of the most commonly tested conceptual traps in basic mechanics.
- Projectile MotionProjectile motion combines two independent motions: constant horizontal velocity and vertically accelerated motion due to gravity.
- Worked Example: Average SpeedHalf a distance at speed v₁, the other half at v₂: average speed is NOT (v₁+v₂)/2. It’s 2v₁v₂/(v₁+v₂), always lower than the plain average, since more time is spent at the slower speed.
- Worked Example: AccelerationA bus reaching 20 km/h in 10 minutes (1/6 hour) has acceleration 20 ÷ (1/6) = 120 km/h² — always convert to matching time units first.
- Building IntuitionUnderstanding graphs of motion builds intuition that extends directly to more advanced topics like calculus-based kinematics.
📝 Exam Point of View
Exam Point of View
- CDS-2 2025, Q22Average speed over equal halves of a journey is 2v₁v₂/(v₁+v₂) — not the plain average (v₁+v₂)/2, a trap almost every option list includes. View this question on the full CDS-2 2025 paper →
- CAPF (ACs) 2026Two cars start from rest; their v-t graph lines make 30° and 60° with the time axis. Since v = (slope) × t, at t=10s: v = 10 tan(30°) and 10 tan(60°). Their difference is 20/√3 m/s. View this question on the full CAPF (ACs) 2026 paper →
- CDS-II 2021, Q22A bus reaching 20 km/h in 10 minutes accelerates at 120 km/h² — the trap is forgetting to convert 10 minutes into hours before dividing. View this question on the full CDS-II 2021 paper →
- CDS-II 2021, Q6A circular-track puzzle: after whole laps (60s = 3 laps here), displacement is zero; after a half lap (10s), displacement equals the track’s diameter, 100 m. View this question on the full CDS-II 2021 paper →
- CDS-I 2023, Q9The area under a velocity-time graph gives net displacement, not distance travelled — the two only match when velocity never reverses sign. View this question on the full CDS-I 2023 paper →
- The PatternKinematics questions love disguising a short calculation as a definitional one, and love testing circular or repeated motion specifically because it splits distance from displacement so cleanly.
- NDA & NA (I) 2018 GAT, Q53For an object moving at constant velocity, speed does NOT change with time — that is the false statement among the options. Constant velocity means fixed speed and direction, zero acceleration, and displacement growing linearly with time. Test yourself on this question
- NDA & NA (I) 2018 GAT, Q54For v = u + at plotted as velocity (y) vs time (x), u is the y-intercept, not the slope — the slope is the acceleration a. Test yourself on this question
- NDA & NA (I) 2025 GAT, Q145Asked which equation of motion is wrong. The answer is “u squared minus v squared equals 2as” — the correct form is v squared minus u squared equals 2as. Test yourself on this question
Related Topics
- GenSci0001 — Physics Fundamentals for Competitive Exams — covers Newton’s laws, the force concept this article’s acceleration builds directly on.
- GenSci0011 — Units, Measurement and Dimensions — the scalar/vector distinction this article applies specifically to motion.
- CDS-II 2021 GK Paper — contains both the acceleration and circular-track displacement PYQs cited above.
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