Subtopics - Motion In One Dimension (NEET)
Four major blocks: the language of motion (position, rest, distance and displacement), kinematic quantities and their graphical representation (speed, velocity, acceleration, x-t and v-t graphs), the five equations of uniform acceleration including free fall under gravity, and relative velocity with river-crossing geometry.
1) Position, Rest, Motion, Distance and Displacement
Defines the coordinate framework for all kinematics: position vector r = xi + yj + zk, the relativity of rest and motion (frame-of-reference dependence), the three types of motion classified by degrees of freedom, and the critical distinction between distance (scalar, path length, always non-negative) and displacement (vector, change in position, can be negative, path-independent). The key inequality distance is greater than or equal to magnitude of displacement governs when average speed equals average velocity.
2) Speed, Velocity, Acceleration and Graphs
Defines and contrasts the four types of speed (uniform, non-uniform, average, instantaneous), the four types of velocity (average, instantaneous, uniform, non-uniform), and acceleration (average delta-v over delta-t, instantaneous dv/dt = d-squared-x/dt-squared). Derives the chain-rule form a = v times dv/dx and the peak-velocity formula for alpha-beta acceleration-deceleration problems. Explains position-time graph (slope = velocity), velocity-time graph (slope = acceleration; area = displacement).
3) Equations of Kinematics and Free Fall Under Gravity
Derives and applies all five equations of motion for uniform acceleration: v = u+at; s = ut+half at-squared; v-squared = u-squared+2as; s = (u+v)t/2; sn = u+a/2 times (2n minus1). Applies them to idealised free-fall. For body dropped from rest: distances at t, 2t, 3t in ratio 1:4:9; distances in nth second in ratio 1:3:5 (odd integers). For body projected upward: time of ascent, total time of flight, maximum height, and reversal of sign at apex. Also covers motion with variable acceleration using integration.
4) Relative Velocity and River Crossing
Defines relative velocity (v12 = v1 minus v2) and applies it to rain-observer problems and the two canonical river-crossing scenarios. For minimum distance crossing: swimmer aims upstream (cos theta = v_river / v_man) so resultant is perpendicular to bank; time = w divided by square-root of (v_man-squared minus v_river-squared). For minimum time: swimmer aims perpendicular to bank; t = w divided by v_man; drifts downstream by v_river times w divided by v_man. The two cases require completely different formulae — a common NEET error source.
Motion In One Dimension Download Notes & Weightage Plan
For each topic in the Motion In One Dimension chapter below, you get (2) the exact resources to download and how to use them, and (3) a simple importance & time plan so NEET students know what to do first and what to revise last.
Position, Rest, Motion, Distance and Displacement
The definitional vocabulary that underpins all kinematics: frame of reference, types of motion, and the scalar-vector distinction between distance and displacement.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Average velocity = 0 for any round trip (displacement = 0). Average speed = total distance / time — never zero for a body that moved. These two facts are tested in 1 MCQ per 2-3 papers.
- High-risk Area: Claiming average velocity equals average speed when body returns to start — this is wrong. They are equal only for unidirectional straight-line motion.
- Best Practice Style: Make a 2-column flashcard: Distance properties vs Displacement properties. Key line: distance never decreases; displacement can. NEET embeds this in a more complex question.
Speed, Velocity, Acceleration and Graphs
The quantitative description of motion: instantaneous vs average quantities, the chain-rule acceleration form a = v dv/dx, and the graphical toolkit (x-t slope = v; v-t slope = a, area = displacement).
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: v-t graph area = displacement (signed). Chain-rule form a = v dv/dx used for position-dependent acceleration. Alpha-beta result v_max = alpha times beta times t divided by (alpha plus beta) appears in direct MCQ form.
- High-risk Area: Using wrong average formula: for equal time intervals use arithmetic mean; for equal distances use harmonic mean 2v1v2/(v1+v2). NEET disguises which case is which through phrasing.
- Best Practice Style: For each v-t graph find: (1) acceleration at t=2s (slope), (2) displacement from t=0 to t=4s (area). Repeat with 5 different shaped graphs until the process is automatic.
Equations of Kinematics and Free Fall Under Gravity
The computational core of the chapter: all five kinematic equations for uniform acceleration, systematic equation-selection strategy, and their complete application to idealised free fall including ratio results and variable-acceleration integration forms.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: sn = u + a/2 times (2n-1) is the highest-trap formula — it gives displacement in nth second ONLY. Ratio memory: 1:4:9 for cumulative distances at t,2t,3t; 1:3:5 for nth-second interval distances. T = 2u/g and h_max = u-squared/2g for upward projection.
- High-risk Area: The nth-second formula trap: NEET offers s = ut + half-at-squared at t=n as a distractor. That is TOTAL displacement at time n, not the nth-second interval value. The sn formula computes the difference s(n) minus s(n-1).
- Best Practice Style: Solve every free-fall problem twice — once with downward positive and once with upward positive. The numerical answer must be identical; if not, the sign convention is inconsistent. This cross-check catches errors before exams.
Relative Velocity and River Crossing
Vector subtraction applied to observer-frame problems: rain angle, swimmer speed, and the two distinct river-crossing objectives (minimum path vs minimum time) with their different formulae and geometry.
1) Download Packs For This Topic (And How To Use Them)
Don't download everything and forget it. Use these like a small "attack kit": read → highlight → test → revise the same sheet again.
2) Importance, Weightage & Time Allocation (Practical)
Use this to avoid over-studying. This topic is usually low effort, quick return if your recall is clean.
- Scoring Focus: Min-distance: effective speed = square-root of (v_man-squared minus v_river-squared); t = w divided by that speed. Min-time: t = w/v_man regardless of current speed. Quote these from memory without re-deriving under exam conditions.
- High-risk Area: Applying minimum-distance formula when question asks for minimum time and vice versa. NEET gives the same river parameters for both types — formula selection is the only test.
- Best Practice Style: Memorise pairing: minimum TIME maps to perpendicular swim maps to t = w/v_man (no square root in denominator). Minimum DISTANCE maps to angled upstream maps to square root in denominator. One property to remember.
Motion In One Dimension Chapter NEET Traps & Common Mistakes (Topic-Wise)
Each subtopic below is of the Motion In One Dimension chapter and shows what NEET students usually do wrong in NEET examination, a short example of the mistake, and how NEET frames the question to trick you with close options are given below.
Mistake Snapshot (What Students Do Wrong)
- Using s = ut + half at-squared when problem asks for displacement in the nth second:: s = ut + half at-squared gives TOTAL displacement from t=0 to t=n. Displacement in the nth second alone requires sn = u + a/2 times (2n-1). Applying the total formula to a nth-second question gives the cumulative value — this is systematically wrong and NEET always provides the wrong total as a distractor.
- Summing sn over n intervals and presenting it as the nth-second displacement:: sn = u + a/2 times (2n-1) is already the displacement in the nth second alone and must NOT be summed. Summing gives total displacement un + half an-squared, which students then present as their answer to a nth-second question.
Body starts from rest with a = 2 m/s-squared. Displacement in the 5th second: sn = 0 + (2/2) times (2 times 5 minus 1) = 1 times 9 = 9 m. WRONG answer using total formula at t=5: s = half times 2 times 25 = 25 m. NEET always puts 25 m as a distractor option. Correct answer = 9 m.
How NEET Frames The Trap
NEET phrases this as 'Find the distance covered in the 5th second of motion.' The word IN signals the nth-second formula. Distractor options always include the total-distance value computed with s = half at-squared.
Q. A particle starts from rest with uniform acceleration of 4 m/s-squared. What is the displacement of the particle in the 4th second of its motion?
A. 32 m B. 14 m C. 16 m D. 28 m
Trick: Using sn = u + a/2 times (2n-1) with u=0, a=4, n=4: s4 = 0 + (4/2) times (8 minus 1) = 2 times 7 = 14 m. Option B is correct. Option A = 32 m is the TOTAL displacement at t=4s using s = half times 4 times 16 = 32 m — wrong formula for this question.
Mistake Snapshot (What Students Do Wrong)
- Forgetting to write a = minus g when upward is taken as positive:: Students who take upward as positive but write a = plus g instead of a = minus g will get wrong velocity at every time step during ascent. Correct setup for upward-positive: a = minus 9.8 m/s-squared always. This single error corrupts all five kinematic equations for the upward phase.
- Claiming acceleration = 0 at maximum height:: At maximum height, velocity = 0 momentarily, but acceleration due to gravity = g downward throughout the entire trajectory including at the top. Acceleration never becomes zero for a freely falling body in the vicinity of Earth.
Ball thrown upward with u = 20 m/s. Time to reach max height: taking up positive, a = minus 10 m/s-squared; 0 = 20 + (minus 10)t gives t = 2 s. With a = plus 10 (wrong sign): 0 = 20 + 10t gives t = minus 2 s. Negative time is physically impossible; students who use the magnitude get 2 s accidentally correct but for wrong reasons.
How NEET Frames The Trap
NEET gives a vertically thrown body and asks height after given time. Options include value with correct g-sign and value with incorrect sign — both are plausible-looking numbers.
Q. A stone is thrown vertically upward with velocity 30 m/s. Taking g = 10 m/s-squared, what is the height above start after 4 seconds?
A. 120 m B. 40 m C. 20 m D. 80 m
Trick: Upward positive: u = 30, a = minus 10, t = 4. s = 30 times 4 + half times (minus 10) times 16 = 120 minus 80 = 40 m. Option B correct. Option A (120 m) ignores the deceleration term entirely. The correct sign gives exactly 40 m.
Mistake Snapshot (What Students Do Wrong)
- Equating average speed with average velocity for a body that returns to its starting point:: Average velocity = net displacement divided by total time. For a round trip displacement = 0, so average velocity = 0. Average speed = total distance divided by total time and is never zero as long as the body moved. Students who apply the same formula to both get average speed = 0, which is wrong.
- Using average velocity = (v1 + v2) divided by 2 for all cases:: This formula holds ONLY for uniform acceleration (linear v-t graph). For non-uniform acceleration or for unequal time intervals at constant speeds, this formula gives wrong results. The general formula is always v_avg = delta-r divided by delta-t.
Car travels 60 km east in 1 hour, then returns 60 km in 2 hours. Average speed = 120 km divided by 3 h = 40 km/h. Average velocity = 0 km divided by 3 h = 0 km/h (displacement = 0). NEET asks for average velocity; students compute average speed and pick 40 km/h — wrong.
How NEET Frames The Trap
NEET precisely describes a round-trip motion and asks for average velocity. Distractor options include the average speed calculated from the same numbers — easy to compute, looks correct, is wrong.
Q. A particle moves from A to B covering 10 m in 2 s, then returns from B to A covering 10 m in 3 s. What are its average speed and average velocity for the entire journey?
A. 4 m/s and 4 m/s B. 4 m/s and 0 m/s C. 0 m/s and 0 m/s D. 3.3 m/s and 3.3 m/s
Trick: Total distance = 20 m; total time = 5 s. Average speed = 20/5 = 4 m/s. Net displacement = 0 (returns to A). Average velocity = 0/5 = 0 m/s. Answer = Option B. Option A gives both values as 4 m/s and fails to distinguish speed from velocity.
Mistake Snapshot (What Students Do Wrong)
- Using t = w / v_man for minimum distance instead of w divided by square-root of (v_man-squared minus v_river-squared):: t = w / v_man gives minimum TIME when swimmer goes perpendicular to bank. For minimum DISTANCE the swimmer must aim upstream and effective crossing speed is reduced to square-root of (v_man-squared minus v_river-squared). Using v_man for minimum-distance problem overestimates effective speed and gives a time that is too short.
- Not checking whether minimum-distance crossing is possible:: Minimum distance crossing (straight across) is only possible if v_man is strictly greater than v_river. If swimmer speed is at most equal to current speed the swimmer cannot cross straight — always drifts downstream.
River width = 100 m; current = 3 m/s; swimmer = 5 m/s in still water. Minimum time: swim perpendicular; t = 100/5 = 20 s; drift = 3 times 20 = 60 m downstream. Minimum distance: aim upstream; effective speed = square-root of (25 minus 9) = 4 m/s; t = 100/4 = 25 s; path = 100 m straight across. Swapping formulas gives wrong answers for both cases.
How NEET Frames The Trap
NEET provides v_swimmer and v_river and asks minimum time to cross. The trap is applying the square-root formula (minimum-distance formula) which gives a longer time — 25 s rather than 20 s. Correct minimum-time answer is the simpler w / v_swim.
Q. A swimmer can swim at 5 m/s in still water. A river of width 40 m flows at 3 m/s. What is the minimum time required to cross the river?
A. 10 s B. 8 s C. 5 s D. 12.5 s
Trick: Minimum time: swim perpendicular to bank. t = 40/5 = 8 s. Option B correct. Option A = 10 s uses effective velocity square-root of (25 minus 9) = 4 m/s which belongs to the minimum-DISTANCE formula — wrong formula for this question.