Complete Math AS Mechanics 1 Mastery: Alternative to Tuition

Explore the difference between vector and scalar quantities, defining magnitude and direction, and distinguish distance, displacement, speed, velocity, acceleration, and time with clear examples.

Learn how displacement-time graphs use slope to represent velocity, identify zero and constant velocity, and analyze changing slopes to reveal acceleration through tangents.

Sketch a displacement-time graph for a particle: 3 m/s for 5 s, stationary 6 s, then -6 m/s back to its initial position, using s=vt and v=Δs/Δt.

Analyze velocity-time graphs by identifying the gradient as acceleration and the area under the graph as displacement, including zero acceleration, constant velocity, and positive or negative (deceleration) acceleration.

Learn to interpret velocity-time graphs by treating gradient as acceleration and area under the graph as displacement. Read velocities at key times, identify zero and negative acceleration, and compute displacement.

Explore acceleration time graphs, where the area under the curve equals the change in velocity. Analyze constant and negative accelerations, including speeding up, slowing, stopping, and reversing.

Analyze the unicorn’s acceleration-time graph, using the area under the curve to find velocity changes, final speed at 30 s, and the total distance of 526 m.

Compare average velocity and average speed by defining displacement and total distance, then compute them from start to end and from the whole journey using a cyclist example.

Define displacement, velocity, and acceleration; derive the five constant-acceleration kinematics equations, including v = u + a t and s = ut + 1/2 a t^2.

Learn to solve constant acceleration questions with worked examples, using v = u + a t, s = ut + 1/2 a t^2, and sign conventions.

Explore vectors and unit vectors, focusing on magnitude and direction, and learn to write vectors in unit-vector form using i and j with examples like a=2i, b=3j, and c=i+j.

Add and subtract vectors using i and j components, draw vectors on the Cartesian plane, and compute sums and differences in unit-vector and vector notations.

Learn that parallel vectors differ by a constant factor a = k b, and apply this to find k when c + k d is parallel to i + j.

Compute vector magnitude and direction on the x–y plane using Pythagoras and tan inverse, and obtain the resultant by summing the i and j components.

Explore bearings by locating north at a reference point, determining bearing angles clockwise, and computing vector bearings from components, magnitudes, and three-digit bearings such as 034, 240, and 304.

Learn how velocity is a vector, compute speed as the magnitude of velocity, and relate displacement, velocity, and acceleration through differentiation and integration with practical examples.

Compute vector with s = s0 + v t, using s0 = 2I + 2J and v = 3I + J; at t = 2, s = 8I + 4J.

Master vector worked examples in mechanics, solving position vectors, velocity, acceleration, speed, and forces using s0 plus vt, and v equals u plus at, and F equals ma.

Solve typical vectors exam problems by deriving position and displacement vectors, computing velocities, and analyzing distances between moving ships to assess sight, collision, and bearing scenarios.

Solves vector past paper questions on motion: determine speed from velocity magnitude, express position as a0+vt, find when the ball is north of B and compute interception velocity, plus bearing.

Represent forces as vectors with magnitude and direction, compute the resultant force by summing horizontal and vertical components, and determine the net force and its direction.

Compute resultant forces and apply Newton's second law to relate mass, acceleration, and net forces; recognize equilibrium when sigma forces cancel.

Newton's first law states that a body remains in equilibrium, at rest or moving with constant velocity, until an external resultant force acts to produce acceleration.

Newton's third law of motion states that for every action there is an equal and opposite reaction, as shown by a hammer and nail and the ground's normal force.

Explore the types of forces, including applied, normal, and tension, and illustrate how weight, gravity, friction, and air resistance are modeled with free body diagrams.

explain how friction force varies from zero to a maximum f max = mu times the normal reaction, to keep the box in equilibrium or signal the onset of sliding.

resolve forces by calculating x and y components and the resultant, using cosine and sine for components and adopting slope-aligned axes to simplify incline problems.

Master horizontal dynamics by resolving forces, calculating normal reaction and friction, and applying f = ma and v^2 = u^2 + 2as in sledge and box problems with angled ropes.

Explore dynamics problems on inclined planes, using F=ma to resolve forces parallel and perpendicular to the slope, including friction, normal reaction, and acceleration calculations.

Analyze dynamics of connected particles over a light, smooth pulley to determine tensions and accelerations, then apply combined dynamics and kinematics to a string-break scenario.

Explore dynamics problems with connected particles, using a system approach to a car and trailer tow, analyze tension in a light inextensible rope, and apply constant-acceleration and brake scenarios.

Explore thrust in a car–trailer system on a horizontal road, using free body diagrams to find acceleration and tow-bar tension, then analyze braking with a thrust of 100 N.

Explore statics and equilibrium, where acceleration is zero. Distinguish dynamics from static problems, and learn that opposite forces balance so the resultant is zero at rest.

Master statics through worked past paper examples, using free-body diagrams, equilibrium equations, and force resolution to compute mass, friction, and tensions in pulley systems.

Learn statics and dynamics through a past papers worked example: resolving forces, finding the resultant, and analyzing equilibrium and motion on an inclined plane with free-body diagrams and normal reaction.

Master statics through past paper problems on a particle on a rough incline with friction, resolving forces in equilibrium to find the normal reaction, force P, tension, and weight.

Explore statics and static equilibrium through a worked example of a heavy package on a rough inclined plane, calculating minimum tension, friction, and tension components in a rope system.

We define momentum as mass times velocity, showing that greater speed or mass yields higher momentum, with the SI unit kilogram meter per second.

The lecture defines impulse as the change in momentum during a collision of mass m, from velocity u to v. It shows impulse over time equals force, F = Δp/Δt.

Apply the conservation of momentum to collisions, equating momentum before and after. Solve for the post-collision velocity of P using the given masses and speeds.

Explore exam-style conservation of momentum problems with two masses 2 kg and 4 kg colliding on a smooth surface, solving for post-collision velocities and impulse using right as positive.

Apply conservation of momentum to two particles on a smooth surface, solve for final velocities, and determine impulse directions between A and B in worked examples.

Apply conservation of momentum to joined particles after collision, treating them as a single mass with a common velocity; study examples with trucks and impulse calculations.

Apply conservation of momentum to two particles connected by a light inextensible string, find their common speed after the string goes taut, and analyze the impulse transmitted through the string.

Explore momentum and impulse problems from past papers on a frictionless horizontal plane, using momentum conservation to find velocity changes and impulse magnitudes.

This lecture uses momentum conservation and impulse to solve collision problems, including two trucks and a railway truck scenario, computing final speeds, masses, and impulse directions.

explore moments as the turning effect of a force about a pivot, calculated as force times the perpendicular distance, with clockwise and anticlockwise directions.

Solve resultant moments about a point by summing positive anticlockwise and negative clockwise moments from forces on a rigid rod, using perpendicular distances and a seesaw intuition.

Compute the reaction forces at supports C and D for a uniform rod in horizontal equilibrium by applying sum of forces and moments; use smart moment points to simplify analysis.

Explore how a uniform rod distributes weight via the center of mass in the middle, then apply the particle concept and tilting about a point with two supports to moments.

analyze past paper moments questions on a uniform plank in equilibrium, using force and moment balance to find support reactions and the mass required to tip about c.

Solve moments and equilibrium problems on a loaded plank using the plank weight and attached load. Determine rope tensions and distances from a past paper scenario.

analyze moments in past paper questions on a non-uniform horizontal rod in equilibrium, find center of mass x and weight w using reactions at C and D and moment equations.

Explore energy in mechanics by examining kinetic energy and gravitational potential energy, using one-half m v squared and m g h with g = ten, measured in joules.

Learn how work is the energy transfer when a force moves a body, calculated as force times distance times cosine theta in joules, with energy conservation and friction considerations.

Compare two scenarios with the same work but different times to see how power differs, using p = w/t and p = f v, in watts.

Apply the work-energy principle, derived from conservation of energy, using the equation work in minus work out equals the change in kinetic energy, including external forces and friction.

Explains the work-energy principle using past paper questions, showing how to calculate work done against resistance, changes in kinetic and potential energy, and the roles of mass, height, and velocity.

Apply the work-energy principle to two connected particles p and q on inclined planes, with a light inextensible string over a smooth pulley and a 0.8 N push.

Analyze past paper questions on power, work, kinetic and potential energy, using the work-energy principle and sigma F = ma to solve constant-speed and resistive-force problems.

Analyze the may–june 2022 9709 mechanics paper 41, applying kinematics, velocity-time graphs, forces, tension, and equilibrium to solve four questions.

Use the work-energy principle to relate driving forces, resistances, and kinetic energy on a horizontal track, then apply power and momentum concepts to collisions and turning points.

Solve Edexcel January 2023 mechanics questions on a train's speed-time graph, acceleration and distance; apply momentum conservation and vector kinematics to collision and velocity problems.

Explore Edexcel mechanics past paper problems on rod equilibrium and center of mass in non-uniform beams, with moment analysis and tilting about supports.

Resolve forces on incline to get acceleration up the plane and speed at B; removing the pull means the particle won't rest at C since 2g sin30 exceeds mu r.

Define modeling assumptions and keywords for mechanics tests, including particles and rods, lamina, rigid, light strings and pulleys, inextensible taut strings, smooth versus rough surfaces, friction, gravity, and collisions.