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CELE Engineering MechanicsDynamics: KinematicsCheat Sheet

Cheat sheet for CELE Engineering Mechanics — Dynamics: Kinematics. Compact, printable, and organised around the concepts Professional Regulation Commission (PRC) — Board of Civil Engineering tests most frequently in the CELE 2026. Perfect for the week before exam day.

Exam context

On the CELE 2026, the Engineering Mechanics subtest carries a "Core" weight in Professional Regulation Commission (PRC) — Board of Civil Engineering's pattern. Dynamics: Kinematics lands at position 7th out of 8 in the standard review order. Target score is 70% weighted average, no sub-test below 50%, and roughly a meaningful share of items come from Engineering Mechanics on a typical CELE paper.

Dynamics: Kinematics - Cheat Sheet

Your last-minute revision companion for kinematics: rectilinear motion, projectile motion, and rotational kinematics. All formulas, conversions, and exam pitfalls condensed for rapid recall in the final 30 minutes.

Sections

Formulas

Formula

v = v₀ + at

Meaning

v = final velocity (m/s); v₀ = initial velocity (m/s); a = acceleration (m/s²); t = time (s)

Watch Out

Sign of a: negative means deceleration (slowing down). Be consistent with your positive direction.

When To Use

When finding velocity after a known time interval with constant acceleration.

Formula

s = v₀t + ½at²

Meaning

s = displacement (m); v₀ = initial velocity (m/s); a = acceleration (m/s²); t = time (s)

Watch Out

This is DISPLACEMENT, not distance. Direction matters. If motion reverses, use calculus.

When To Use

When finding displacement over a time interval; use this when time is known.

Formula

v² = v₀² + 2as

Meaning

v = final velocity (m/s); v₀ = initial velocity (m/s); a = acceleration (m/s²); s = displacement (m)

Watch Out

This equation works only for CONSTANT acceleration. Cannot directly find v if a varies with position.

When To Use

When you know displacement and acceleration but NOT time. Eliminates t from the problem.

Formula

a = (v − v₀)/t = Δv/Δt

Meaning

Average acceleration is the change in velocity divided by time elapsed.

Watch Out

For variable acceleration, this gives AVERAGE a, not instantaneous a. Use calculus for instantaneous.

When To Use

Rearrange to find time or initial velocity when acceleration is constant.

Common Values

Value

9.81 m/s² or 9.80 m/s² (often 10 m/s² for approximation)

Symbol

g

Quantity

Acceleration due to gravity (standard)

Section Title

Rectilinear Motion — Constant Acceleration

Important Facts

  • The three kinematic equations (v = v₀ + at, s = v₀t + ½at², v² = v₀² + 2as) are interrelated; each omits one variable.
  • Constant acceleration is the only case where these simple formulas apply directly; variable acceleration requires integration.
  • For free fall, use a = g = 9.81 m/s² (downward is positive if you define downward as +y).
  • v–t graphs: slope = acceleration; area under curve = displacement.
  • s–t graphs: slope = velocity; curvature indicates acceleration (parabolic for constant a).

Key Definitions

Term

Displacement (s)

Example

Car moves 50 m east then 20 m west: displacement = 30 m east; distance = 70 m.

Definition

Vector quantity representing the change in position; can be negative (opposite direction).

Term

Velocity (v)

Example

v = ds/dt; instantaneous velocity at t = 2 s is the slope of the s–t curve at that point.

Definition

Rate of change of displacement with respect to time; includes direction (vector).

Term

Acceleration (a)

Example

Constant deceleration of −4 m/s² means velocity decreases by 4 m/s every second.

Definition

Rate of change of velocity with respect to time; a = dv/dt = v(dv/ds).

Term

Deceleration

Example

Car braking: a = −4 m/s² (if forward is positive).

Definition

Acceleration in the direction opposite to velocity; represented as negative acceleration.

Diagrams To Know

  • v–t (velocity vs. time) graph for constant acceleration: straight line with slope = a.
  • s–t graph for constant acceleration: parabola (upward if a > 0, downward if a < 0).
  • a–t graph for constant acceleration: horizontal line at constant value.

Formulas

Formula

v = ∫a dt

Meaning

Velocity is the integral of acceleration with respect to time; add constant of integration.

Watch Out

Must know the initial condition (v at t = 0) to evaluate the constant of integration.

When To Use

When acceleration is a function of time: a = a(t).

Formula

s = ∫v dt

Meaning

Displacement is the integral of velocity with respect to time.

Watch Out

Two levels of integration: first a → v, then v → s. Each adds an integration constant.

When To Use

After finding v(t), integrate to get s(t). Again, use initial position s₀.

Formula

a = v(dv/ds)

Meaning

Acceleration expressed as a function of position: use when a = a(s).

Watch Out

This is an alternative form of a = dv/dt; rearrange and separate variables to solve.

When To Use

When acceleration depends on position, not time. Relates a, v, and s directly.

Section Title

Rectilinear Motion — Variable Acceleration

Important Facts

  • When a is given as a function of time a(t), integrate twice: v = ∫a dt, then s = ∫v dt.
  • When a is given as a function of position a(s), use a = v(dv/ds) and separate variables.
  • Always evaluate constants of integration using initial conditions (v₀ at t = 0, s₀ at t = 0).
  • Board exams rarely give complex variable-a problems; most are constant-a disguised as variable.

Key Definitions

Term

Variable acceleration

Example

a = 2t (acceleration increases linearly with time); a = kv (air resistance proportional to velocity).

Definition

Acceleration that changes with time, position, or velocity; requires calculus to solve.

Diagrams To Know

  • Curved v–t graph: slope at any point = instantaneous acceleration a(t).
  • Area under a–t graph from t₁ to t₂ = change in velocity Δv.

Formulas

Formula

v = gt (or v = v₀ + gt for non-zero initial velocity)

Meaning

v = velocity at time t; g = 9.81 m/s² (downward positive); v₀ = initial velocity.

Watch Out

Sign convention: define downward as + or −, then be consistent. Upward throws start with −v₀.

When To Use

Object dropped or thrown vertically; assume no air resistance.

Formula

h = v₀t + ½gt²

Meaning

h = vertical height fallen (m); v₀ = initial upward velocity (m/s); t = time (s); g = 9.81 m/s².

Watch Out

If thrown upward, v₀ > 0 and h decreases initially; ½gt² always opposes the chosen direction.

When To Use

Finding height or depth after time t in vertical motion.

Formula

v² = v₀² + 2gh

Meaning

Final velocity squared in terms of height fallen; links velocity and height without time.

Watch Out

If thrown upward, v₀ is positive; at max height, v = 0 and h = h_max.

When To Use

When time is unknown; most common in impact-speed problems.

Formula

t_total = (2v₀)/g (object thrown upward, returns to starting height)

Meaning

Time of flight for symmetric projectile launched and landing at same height.

Watch Out

Applies ONLY if launch and landing heights are equal. Different heights: solve h = 0 directly.

When To Use

Vertical launch with upward initial velocity v₀.

Common Values

Value

14.0 m/s

Symbol

v = √(2·9.81·10)

Quantity

Impact speed from 10 m height (dropped from rest)

Value

1.43 s

Symbol

t = √(2·10/9.81)

Quantity

Time to fall 10 m from rest

Section Title

Free Fall and Vertical Motion

Important Facts

  • At maximum height, v = 0; use v² = v₀² + 2gh or v = v₀ − gt to find time to max height.
  • On return to starting height, final speed equals initial speed (by energy symmetry); direction is opposite.
  • Air resistance is ALWAYS ignored in kinematics unless explicitly stated.
  • Impact speed from height h (dropped from rest): v = √(2gh). For h = 10 m, g = 9.81, v ≈ 14 m/s.

Key Definitions

Term

Free fall

Example

Stone dropped from cliff or ball thrown upward (both experience g throughout motion).

Definition

Motion under gravity alone, with no air resistance; acceleration = g = 9.81 m/s² downward.

Diagrams To Know

  • Vertical motion graphs: v–t is a straight line (slope = −g if upward is +); s–t is inverted parabola.

Formulas

Formula

x = (v₀ cos θ)t

Meaning

Horizontal displacement; v₀ = launch speed (m/s); θ = launch angle; t = time (s).

Watch Out

Horizontal velocity NEVER changes (no air resistance). This is NOT accelerated motion.

When To Use

Horizontal motion is uniform (constant velocity); find how far projectile travels horizontally.

Formula

y = (v₀ sin θ)t − ½gt²

Meaning

Vertical displacement above launch point; second term is gravity effect.

Watch Out

At landing, y = 0 (if landing at same height); solve for t, then find range via x = (v₀ cos θ)t.

When To Use

Vertical motion includes gravity; describe height at any time t.

Formula

R = (v₀² sin 2θ)/g

Meaning

Range (horizontal distance): applies when projectile lands at same height as launch.

Watch Out

Uses sin 2θ, NOT sin² θ. Maximum range at θ = 45°. Complementary angles (e.g., 30° and 60°) give same range.

When To Use

Find how far a projectile travels horizontally (landing height = launch height).

Formula

H = (v₀² sin² θ)/(2g)

Meaning

Maximum height above launch point; vertical component only.

Watch Out

Uses sin² θ (different from range formula). At max height, v_y = 0; time to max height = (v₀ sin θ)/g.

When To Use

Find peak height of trajectory.

Formula

t_flight = (2v₀ sin θ)/g

Meaning

Total time in air for symmetric trajectory (landing at same height).

Watch Out

This is exactly twice the time to reach max height: t_max = (v₀ sin θ)/g.

When To Use

Find how long projectile is airborne.

Formula

v_x = v₀ cos θ (constant)

Meaning

Horizontal component of velocity remains constant throughout flight.

Watch Out

ALWAYS constant. Vertical component v_y changes due to gravity.

When To Use

Analyze velocity at any instant; horizontal component never changes.

Formula

v_y = v₀ sin θ − gt

Meaning

Vertical component of velocity at time t; decreases due to gravity.

Watch Out

Positive upward. At landing (if same height), v_y = −v₀ sin θ (downward, same magnitude as launch).

When To Use

Find vertical velocity at any time; becomes zero at max height.

Formula

v = √(v_x² + v_y²)

Meaning

Magnitude of total velocity at any instant; combine components vectorially.

Watch Out

Speed is scalar (magnitude only). Use Pythagoras to combine perpendicular components.

When To Use

Find speed (not velocity component) at a given time or position.

Common Values

Value

91.7 m

Symbol

R = (900 × sin 90°)/9.81

Quantity

Range at 45° launch with v₀ = 30 m/s

Value

22.9 m

Symbol

H = (900 × sin² 45°)/(2 × 9.81)

Quantity

Max height at 45° launch with v₀ = 30 m/s

Value

4.33 s

Symbol

t = (2 × 30 × sin 45°)/9.81

Quantity

Flight time at 45° launch with v₀ = 30 m/s

Section Title

Projectile Motion

Important Facts

  • Horizontal and vertical motions are INDEPENDENT: solve them separately and combine results via time t.
  • Maximum range occurs at θ = 45° for symmetric trajectories: R_max = v₀²/g.
  • Complementary angles θ and (90° − θ) give the same range but different max heights and flight times.
  • At max height, v_y = 0 but v_x ≠ 0; speed is not zero, only vertical component is.
  • Landing speed (if landing at same height) has same magnitude as launch speed but different direction.
  • If landing height ≠ launch height, solve y = (v₀ sin θ)t − ½gt² for t when y = height difference, then find x.

Key Definitions

Term

Projectile

Example

Thrown ball, launched rocket, or water from a fountain; all follow parabolic paths.

Definition

Object moving under gravity alone, with initial velocity at an angle; horizontal and vertical motions are independent.

Term

Range (R)

Example

Soccer kick with v₀ = 20 m/s at 45°: R = (400 × sin 90°)/9.81 ≈ 40.8 m.

Definition

Horizontal distance traveled by projectile, from launch to landing at same height.

Term

Maximum height (H)

Example

Ball thrown upward at 20 m/s: H = (400 × sin² 90°)/(2 × 9.81) ≈ 20.4 m (if θ = 90°).

Definition

Peak vertical displacement above the launch point; occurs when v_y = 0.

Diagrams To Know

  • Parabolic trajectory: symmetric if landing = launch height; longer on one side if landing lower.
  • v–t components: v_x is constant horizontal line; v_y is a downward-sloping line (slope = −g).
  • Velocity vector at any point: combine v_x (horizontal) and v_y (vertical) components.

Formulas

Formula

ω = ω₀ + αt

Meaning

ω = final angular velocity (rad/s); ω₀ = initial angular velocity (rad/s); α = angular acceleration (rad/s²); t = time (s).

Watch Out

Must use radians, not degrees or revolutions. Sign of α: negative means deceleration (slowing rotation).

When To Use

Constant angular acceleration; find angular velocity after known time.

Formula

θ = ω₀t + ½αt²

Meaning

θ = angular displacement (rad); ω₀ = initial angular velocity (rad/s); α = angular acceleration (rad/s²); t = time (s).

Watch Out

θ is in RADIANS. Convert revolutions: 1 rev = 2π rad. If α varies, integrate ω instead.

When To Use

Constant angular acceleration; find angular displacement over time interval.

Formula

ω² = ω₀² + 2αθ

Meaning

Final angular velocity squared in terms of angular displacement; eliminates time.

Watch Out

Again, use radians for θ. This is the rotational analogue of v² = v₀² + 2as.

When To Use

When time is unknown; links angular velocity and displacement.

Formula

α = (ω − ω₀)/t

Meaning

Angular acceleration is the change in angular velocity per unit time.

Watch Out

For constant α. If α varies with time or position, use calculus (α = dω/dt or α = ω dω/dθ).

When To Use

Solve for α, ω₀, or t when others are known.

Common Values

Value

ω (rad/s) = (2π × rpm)/60 ≈ 0.10472 × rpm

Symbol

rpm ↔ rad/s

Quantity

Conversion: revolutions per minute to radians per second

Value

31.42 rad/s

Symbol

ω = (2π × 300)/60

Quantity

300 rpm in rad/s

Section Title

Rotational (Angular) Kinematics

Important Facts

  • Rotational equations mirror rectilinear ones: (θ, ω, α) ↔ (s, v, a); use same three-equation set.
  • ALWAYS convert rpm or Hz to rad/s before using kinematic equations: ω (rad/s) = (2π × N)/60 where N is rpm.
  • Revolutions: 1 rev = 2π rad. To find revolutions, calculate θ in radians and divide by 2π.
  • Angular velocity and acceleration can be positive (counterclockwise) or negative (clockwise); define positive direction first.
  • Constant angular acceleration is common in rotors, motors, and flywheels; variable α requires integration.

Key Definitions

Term

Angular velocity (ω)

Example

Flywheel rotating at 300 rpm ≡ ω = (2π × 300)/60 = 31.42 rad/s.

Definition

Rate of change of angular position (angle) with respect to time; ω = dθ/dt (rad/s).

Term

Angular acceleration (α)

Example

Motor accelerating from 0 to 1500 rpm in 5 s: α ≈ 31.4 rad/s² (convert rpm to rad/s first).

Definition

Rate of change of angular velocity with respect to time; α = dω/dt (rad/s²).

Term

Radian (rad)

Example

A wheel rotating 2 revolutions = 4π rad ≈ 12.57 rad.

Definition

Unit of angle in kinematics; 1 rev = 2π rad ≈ 6.283 rad; 1 rad ≈ 57.3°.

Diagrams To Know

  • ω–t (angular velocity vs. time) graph: straight line for constant α (slope = α).
  • θ–t graph: parabola for constant α; curvature indicates direction and magnitude of α.

Formulas

Formula

s = rθ

Meaning

Arc length s (m) traveled by a point at radius r (m) through angle θ (rad).

Watch Out

θ MUST be in radians, not degrees. If θ is in degrees, convert: θ_rad = θ_deg × π/180.

When To Use

Convert angular displacement to arc length for a point on a rotating object.

Formula

v = rω

Meaning

Linear (tangential) velocity v (m/s) of a point at radius r (m) rotating with angular velocity ω (rad/s).

Watch Out

ω must be in rad/s. This is the TANGENTIAL velocity (along the circle), not radial.

When To Use

Convert angular velocity to linear speed at any radius; essential for gears, pulleys, wheels.

Formula

a_t = rα

Meaning

Tangential acceleration a_t (m/s²) at radius r due to angular acceleration α (rad/s²).

Watch Out

This is TANGENTIAL (along motion), not the centripetal acceleration a_n = v²/r pointing inward.

When To Use

Find the linear acceleration in the direction of motion (along the circle).

Formula

a_n = v²/r = rω²

Meaning

Normal (centripetal) acceleration a_n (m/s²); directed toward the center; always present in circular motion.

Watch Out

This is NOT zero in circular motion; it exists even at constant ω. Use v²/r if you know linear speed, rω² if angular speed.

When To Use

Find radial acceleration (center-pointing); use either v²/r or rω² depending on what you know.

Formula

a_total = √(a_t² + a_n²)

Meaning

Total acceleration is vector sum of tangential and normal (centripetal) components.

Watch Out

These are perpendicular; use Pythagoras. Do not add magnitudes directly.

When To Use

Find magnitude of total acceleration when both tangential and centripetal components are present.

Common Values

Value

20 m/s²

Symbol

a_n = 100/5

Quantity

Centripetal acceleration for v = 10 m/s, r = 5 m

Section Title

Linking Rotation and Linear Motion

Important Facts

  • For a point on a rotating body: v = rω (tangential), a_n = rω² (centripetal), a_t = rα (tangential rate of change).
  • Centripetal acceleration a_n is ALWAYS present and directed INWARD (toward axis) in any circular motion.
  • Tangential acceleration a_t is zero if ω is constant (uniform circular motion); nonzero if ω is changing (nonuniform).
  • Different points on the same rotating object have different linear speeds v and accelerations a, but same ω and α.
  • In gears or pulleys: the tangential velocity is the same at the meshing points, so v₁ = v₂, thus r₁ω₁ = r₂ω₂.

Key Definitions

Term

Tangential velocity

Example

Rim of a wheel 0.5 m radius rotating at 20 rad/s: v = 0.5 × 20 = 10 m/s (tangent to wheel).

Definition

Linear velocity of a point on a rotating body, directed along the circle (perpendicular to radius); v = rω.

Term

Centripetal (normal) acceleration

Example

Car on a circular track at 15 m/s with radius 50 m: a_n = 225/50 = 4.5 m/s² (toward center).

Definition

Acceleration directed toward the center of rotation; a_n = v²/r = rω²; always nonzero in circular motion.

Term

Tangential acceleration

Example

Wheel accelerating at α = 2 rad/s² at radius 0.3 m: a_t = 0.3 × 2 = 0.6 m/s² (along rim).

Definition

Component of acceleration along the direction of motion; a_t = rα; nonzero only if ω is changing.

Diagrams To Know

  • Rotating body: velocity v is tangent to circle; centripetal a_n points inward; tangential a_t is along velocity direction.
  • Free-body diagram of rotating point: show centripetal acceleration (inward) and tangential acceleration (along motion).

Common Values

Value

2π/60 ≈ 0.10472

Symbol

ω (rad/s) = N × (2π/60) where N is rpm

Quantity

Conversion factor: rpm to rad/s

Value

60/(2π) ≈ 9.549

Symbol

N (rpm) = ω × 60/(2π)

Quantity

Conversion factor: rad/s to rpm

Section Title

Unit Conversions in Kinematics

Important Facts

  • Angular velocity: 1 rpm = (2π/60) rad/s ≈ 0.10472 rad/s; conversely, 1 rad/s ≈ 9.549 rpm.
  • Angular position: 1 rev = 2π rad = 360°; 1 rad ≈ 57.3°; 1° = π/180 rad ≈ 0.01745 rad.
  • Frequency: 1 Hz = 1 rev/s = 60 rpm = 2π rad/s.
  • Time: 1 min = 60 s; hours to seconds and vice versa are rare in kinematics but common in real applications.
  • Speed: 1 m/s = 3.6 km/h; conversely, 1 km/h ≈ 0.278 m/s.

Must Remember

  • The three constant-acceleration kinematic equations are ALWAYS linked; if you know any two of (v, s, t, a), you can find the third using the appropriate equation.
  • For projectile motion, horizontal motion (x = v₀ cos θ · t) is INDEPENDENT of vertical motion (y = v₀ sin θ · t − ½gt²); solve separately, combine via time t.
  • Maximum range in projectile motion occurs at θ = 45° and equals R_max = v₀²/g; complementary angles (e.g., 30° and 60°) yield the same range but different flight times and heights.
  • Angular equations (ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ) mirror linear equations exactly; θ ↔ s, ω ↔ v, α ↔ a.
  • ALWAYS convert rpm to rad/s using ω = (2π N)/60 before plugging into rotational kinematic equations; units are critical.
  • Centripetal (normal) acceleration a_n = v²/r = rω² ALWAYS points toward the center and is ALWAYS nonzero in any circular motion, even if ω is constant.
  • Displacement (vector) and distance (scalar) are different; in kinematics, use displacement s, which can be negative; solve for time first, then check if motion reverses.
  • Free fall or vertical motion: define downward as + or −, then apply g = 9.81 m/s² consistently; upward throws have negative initial velocity under this convention.
  • For variable acceleration, use integration: v = ∫a dt and s = ∫v dt; always evaluate constants of integration using initial conditions (v₀ and s₀).
  • In circular motion of a point: tangential velocity v = rω, tangential acceleration a_t = rα (nonzero only if α ≠ 0), centripetal acceleration a_n = rω² (always nonzero).

Last Minute Tips

  • Double-check unit conversions: rpm → rad/s, degrees → radians. A single unit error cascades through the entire solution. Always state your conversion factor explicitly.
  • For projectile problems, always identify whether launch and landing heights are equal; if not, solve y = (v₀ sin θ)t − ½gt² = Δy for t before finding range. Do NOT use the symmetric-trajectory formulas blindly.
  • In free-fall problems, consistently define your positive direction (up or down) at the START. Then apply g with the correct sign throughout. Sign errors are the #1 mistake on exams.
  • For rotational kinematics, always ask: 'Is ω constant or varying?' If constant, a_n = rω² and a_t = 0. If ω is changing, calculate both a_t = rα and a_n = rω² and find total via Pythagoras.
  • On the exam, use s = v₀t + ½at² or v² = v₀² + 2as depending on what you're given; these are faster than integrating variable acceleration. Save calculus for questions that explicitly give a(t) or a(s).

Comparison Tables

Rows

Values

  • s (m)
  • θ (rad)
  • s = rθ

Property

Position/Displacement

Values

  • v (m/s)
  • ω (rad/s)
  • v = rω

Property

Velocity

Values

  • a (m/s²)
  • α (rad/s²)
  • a_t = rα (tangential)

Property

Acceleration

Values

  • v = v₀ + at
  • ω = ω₀ + αt
  • Direct parallel

Property

1st Equation

Values

  • s = v₀t + ½at²
  • θ = ω₀t + ½αt²
  • Direct parallel

Property

2nd Equation

Values

  • v² = v₀² + 2as
  • ω² = ω₀² + 2αθ
  • Direct parallel

Property

3rd Equation

Columns

  • Quantity
  • Rectilinear (Linear)
  • Rotational (Angular)
  • Link

Table Title

Rectilinear vs. Rotational Kinematics (Constant Acceleration)

Rows

Values

  • Same height
  • t = (2v₀ sin θ)/g
  • R = (v₀² sin 2θ)/g
  • H = (v₀² sin² θ)/(2g)

Property

Symmetric trajectory

Values

  • y = 0 at start and end
  • Solve (v₀ sin θ)t − ½gt² = 0
  • Use symmetric formulas
  • Occurs at t = (v₀ sin θ)/g

Property

Launch from ground level

Values

  • y_land ≠ y_launch
  • Solve y = (v₀ sin θ)t − ½gt² = Δy
  • x = (v₀ cos θ) × t_land
  • Same formula; occurs when v_y = 0

Property

Different heights

Values

  • Same height only
  • θ = 45°
  • R_max = v₀²/g
  • H_45° = v₀²/(4g)

Property

Max range angle

Columns

  • Scenario
  • Launch Height vs. Landing
  • Formula for Time
  • Formula for Range
  • Formula for Max Height

Table Title

Projectile Motion: Key Formulas and Scenarios

Rows

Values

  • Plugging rpm directly into rotational equations
  • Always convert: ω = 2πN/60 where N = rpm
  • Equations require SI units; answers will be off by ~10.

Property

Forgetting to convert rpm to rad/s

Values

  • R = (v₀² sin θ)/g (WRONG)
  • R = (v₀² sin 2θ)/g (CORRECT)
  • Drastically wrong numerical answer; only sin 2θ gives correct range.

Property

Using sin θ instead of sin 2θ for range

Values

  • Treating them as same in calculations
  • Distance is scalar (total path); displacement is vector (net change)
  • Sign and direction matter in rectilinear motion; affects final answer.

Property

Confusing distance and displacement

Values

  • Plugging degrees or revolutions into equations
  • Convert everything to radians before solving
  • Formulas s = rθ, v = rω derived assuming θ in radians; degree use gives wrong results.

Property

Not using radians for angular kinematics

Values

  • Treating deceleration (upward throw) as positive
  • Define direction first, then apply sign consistently
  • Wrong sign → wrong time to max height, wrong impact velocity.

Property

Forgetting sign of acceleration in free fall

Values

  • Assuming a = 0 when ω is constant
  • Centripetal a_n = v²/r = rω² always exists if there's rotation
  • Total acceleration is nonzero even in uniform circular motion.

Property

Ignoring centripetal acceleration in circular motion

Columns

  • Mistake
  • Correct Approach
  • Why It Matters

Table Title

Common Mistakes in Kinematics (Watch-Out Summary)

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