1.1 Kinematics

Irodov Problems 1.1 to 1.58.

58problems
103figures
Difficulty2.8avgDifficulty: 0 rated 1, 19 rated 2, 32 rated 3, 7 rated 4, 0 rated 5; mean 2.8.
Uniqueness3.3avgUniqueness: 0 rated 1, 9 rated 2, 25 rated 3, 20 rated 4, 4 rated 5; mean 3.3.

No.	Title	Difficulty	Uniqueness	Methods
1.1	The Raft Frame Cancels the Unknown	Difficulty 2 of 5	Uniqueness 4 of 5	relative motion · frames of reference
1.2	Half Distance, Half Time, Different Means	Difficulty 2 of 5	Uniqueness 2 of 5	kinematic graphs · limiting cases
1.3	Symmetric Ramps Around an Unknown Plateau	Difficulty 3 of 5	Uniqueness 3 of 5	kinematic graphs · symmetry · limiting cases
1.4	Reading a Motion Graph's Three Speeds	Difficulty 3 of 5	Uniqueness 4 of 5	kinematic graphs · calculus of motion · optimization
1.5	Colliding Particles Share One Line	Difficulty 2 of 5	Uniqueness 2 of 5	relative motion · frames of reference · vector decomposition
1.6	The Triangle Behind a Southeastern Wind	Difficulty 3 of 5	Uniqueness 3 of 5	relative motion · vector decomposition · limiting cases
1.7	Two Routes Across, One Arrival Time	Difficulty 4 of 5	Uniqueness 4 of 5	relative motion · vector decomposition
1.8	Crossing Costs More Than Coasting	Difficulty 3 of 5	Uniqueness 3 of 5	relative motion · vector decomposition
1.9	Aiming Upstream to Minimize Drift	Difficulty 3 of 5	Uniqueness 3 of 5	relative motion · optimization · vector decomposition
1.10	Gravity Cancels, Only Launch Differs	Difficulty 2 of 5	Uniqueness 4 of 5	projectile · relative motion · vector decomposition
1.11	Same Fall Erases the Vertical Gap	Difficulty 2 of 5	Uniqueness 3 of 5	relative motion · vector decomposition · calculus of motion
1.12	A Shrinking Triangle That Never Turns Ninety	Difficulty 3 of 5	Uniqueness 4 of 5	symmetry · relative motion · calculus of motion
1.13	Aim Steadily at a Target That Cannot Turn	Difficulty 4 of 5	Uniqueness 5 of 5	relative motion · calculus of motion · limiting cases
1.14	Two Lights, One Chord, One Frame	Difficulty 3 of 5	Uniqueness 4 of 5	relative motion · frames of reference · kinematic graphs
1.15	The Bolt That Keeps Rising First	Difficulty 3 of 5	Uniqueness 3 of 5	frames of reference · non inertial frame · calculus of motion
1.16	Closest Approach Along Two Perpendicular Rails	Difficulty 2 of 5	Uniqueness 2 of 5	optimization · relative motion · vector decomposition
1.17	Minimizing Time, Not Distance	Difficulty 3 of 5	Uniqueness 4 of 5	optimization · calculus of motion · limiting cases
1.18	One Graph Breeds Three More	Difficulty 2 of 5	Uniqueness 2 of 5	kinematic graphs · calculus of motion
1.19	Mean Speed Outruns Mean Velocity	Difficulty 3 of 5	Uniqueness 4 of 5	circular motion · calculus of motion · vector decomposition
1.20	Turning Point Doubles the Distance	Difficulty 2 of 5	Uniqueness 3 of 5	calculus of motion · symmetry · vector decomposition
1.21	Reversal Splits Distance from Displacement	Difficulty 3 of 5	Uniqueness 2 of 5	calculus of motion · kinematic graphs
1.22	Square-Root Speed, Quadratic Position	Difficulty 3 of 5	Uniqueness 3 of 5	differential equation · calculus of motion · limiting cases
1.23	A Deceleration That Actually Stops	Difficulty 2 of 5	Uniqueness 3 of 5	calculus of motion · differential equation · dimensional analysis
1.24	One Parabola, Constant Acceleration Underneath	Difficulty 2 of 5	Uniqueness 2 of 5	calculus of motion · vector decomposition · kinematic graphs
1.25	Velocity Meets Acceleration at Forty-Five	Difficulty 3 of 5	Uniqueness 3 of 5	calculus of motion · kinematic graphs · vector decomposition
1.26	A Disguised Circle Hides in Sines	Difficulty 2 of 5	Uniqueness 3 of 5	circular motion · calculus of motion
1.27	Reading Launch Speed Off a Parabola's Shape	Difficulty 3 of 5	Uniqueness 3 of 5	calculus of motion · projectile · vector decomposition
1.28	Chords Are Mean Velocities in Disguise	Difficulty 2 of 5	Uniqueness 3 of 5	calculus of motion · projectile
1.29	Reading a Whole Flight from One Launch	Difficulty 3 of 5	Uniqueness 3 of 5	projectile · calculus of motion · vector decomposition
1.30	Two Accelerations Trade Places Mid Flight	Difficulty 3 of 5	Uniqueness 4 of 5	projectile · vector decomposition · kinematic graphs
1.31	Elastic Bounces Walk Down the Slope	Difficulty 3 of 5	Uniqueness 4 of 5	projectile · vector decomposition · calculus of motion
1.32	One Range, Two Flight Times	Difficulty 2 of 5	Uniqueness 2 of 5	projectile · calculus of motion · limiting cases
1.33	Timing the Second Shot to Collide	Difficulty 3 of 5	Uniqueness 4 of 5	projectile · vector decomposition · calculus of motion
1.34	A Wind-Bent Balloon's Two Accelerations	Difficulty 3 of 5	Uniqueness 3 of 5	calculus of motion · vector decomposition · limiting cases
1.35	Curvature Radius from a Velocity Law	Difficulty 3 of 5	Uniqueness 3 of 5	calculus of motion · vector decomposition
1.36	Only the X-Projection Ever Mattered	Difficulty 3 of 5	Uniqueness 4 of 5	calculus of motion · differential equation · vector decomposition
1.37	The Radius Cancels from Total Acceleration	Difficulty 2 of 5	Uniqueness 3 of 5	circular motion · calculus of motion
1.38	Equal Twins: Slowing Down and Turning	Difficulty 3 of 5	Uniqueness 3 of 5	circular motion · differential equation · calculus of motion
1.39	A Constant Tangential Twist in Disguise	Difficulty 2 of 5	Uniqueness 2 of 5	circular motion · calculus of motion · vector decomposition
1.40	Minimum Acceleration Hides Between the Extremes	Difficulty 3 of 5	Uniqueness 3 of 5	circular motion · calculus of motion · optimization
1.41	Curvature Shrinks as Speed Runs Away	Difficulty 3 of 5	Uniqueness 3 of 5	calculus of motion · vector decomposition
1.42	Constant Speed Turns Curvature into Acceleration	Difficulty 3 of 5	Uniqueness 4 of 5	calculus of motion · vector decomposition · limiting cases
1.43	The Chord's Rate Doubles at the Rim	Difficulty 4 of 5	Uniqueness 5 of 5	circular motion · vector decomposition · symmetry
1.44	Radius Cancels, Speed and Time Remain	Difficulty 2 of 5	Uniqueness 3 of 5	circular motion · calculus of motion
1.45	Two Uniform Accelerations Share One Clock	Difficulty 2 of 5	Uniqueness 3 of 5	calculus of motion · circular motion · dimensional analysis
1.46	Averages of a Cubic Rotation Law	Difficulty 3 of 5	Uniqueness 3 of 5	calculus of motion · circular motion · dimensional analysis
1.47	When Acceleration Tips Away from Velocity	Difficulty 3 of 5	Uniqueness 4 of 5	circular motion · vector decomposition · calculus of motion
1.48	A Square Root Deceleration's Mean Speed	Difficulty 4 of 5	Uniqueness 4 of 5	differential equation · calculus of motion · dimensional analysis
1.49	Rotation That Never Quite Finishes	Difficulty 3 of 5	Uniqueness 4 of 5	differential equation · calculus of motion
1.50	An Oscillation Between Two Turning Points	Difficulty 4 of 5	Uniqueness 5 of 5	differential equation · calculus of motion · kinematic graphs
1.51	Where the Instantaneous Axis Actually Sits	Difficulty 3 of 5	Uniqueness 4 of 5	rigid body rotation · calculus of motion · vector decomposition
1.52	Rolling Points Always Accelerate Toward Center	Difficulty 2 of 5	Uniqueness 3 of 5	rolling · circular motion · calculus of motion
1.53	Three Rim Points, One Rigid Body	Difficulty 3 of 5	Uniqueness 3 of 5	rolling · rigid body rotation · vector decomposition
1.54	How Sharply the Rim Points Turn	Difficulty 3 of 5	Uniqueness 4 of 5	rolling · calculus of motion · circular motion
1.55	Two Perpendicular Spins Compose Like Vectors	Difficulty 3 of 5	Uniqueness 4 of 5	vector decomposition · rigid body rotation · frames of reference
1.56	Two Vectors, Seventeen Degrees Apart	Difficulty 2 of 5	Uniqueness 2 of 5	calculus of motion · vector decomposition
1.57	The Line Joining Two Rest Points	Difficulty 4 of 5	Uniqueness 5 of 5	rigid body rotation · rolling · vector decomposition
1.58	When A Spin Axis Itself Precesses	Difficulty 4 of 5	Uniqueness 4 of 5	rigid body rotation · vector decomposition · frames of reference