State the four equations of motion for uniform acceleration, defining each symbol and its unit.

The equations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t, where u is the initial velocity in m s⁻¹, v the final velocity in m s⁻¹, a the uniform acceleration in m s⁻², t the time in seconds and s the displacement in metres.

State the conditions under which the equations of motion may be used.

They apply only when the acceleration is constant in both size and direction, so the motion must be in a straight line with uniform acceleration throughout the interval considered.

Which equation of motion should be chosen when the time taken is neither known nor required?

The equation v² = u² + 2as should be used, because it links initial velocity, final velocity, acceleration and displacement without involving time.

Which equation of motion should be chosen when the final velocity is neither known nor required?

The equation s = ut + ½at² should be used, because it links displacement to initial velocity, acceleration and time without involving the final velocity.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

Topic overview Physical quantities and SI base units Prefixes and standard form Scalars and vectors Resolving vectors and finding resultants Coplanar forces in equilibrium

Moments and Equilibrium

Topic overview Moment of a force Centre of gravity The principle of moments Determining unknown masses using moments

Linear Motion and Dynamics

Topic overview Displacement, velocity and acceleration The equations of motion for uniform acceleration Measuring the acceleration of free fall with light gates Displacement–time and velocity–time graphs Projectile motion Projectile calculations

Newton's Laws of Motion

Topic overview Newton's first law and inertia Newton's second law and F = ma Applying Newton's laws to simple situations Newton's third law Friction as a force opposing motion

Linear Momentum and Impulse

Topic overview Momentum and its calculation Conservation of linear momentum Collisions in one dimension Elastic and inelastic collisions Impulse and the impulse–momentum equation Impacts and reducing the force of a collision Newton's second law in terms of momentum

Work, Energy and Power

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Current, Charge and Potential Difference

Topic overview Electric current and the coulomb Potential difference and energy transfer Potential difference, power and current Electromotive force Comparing electromotive force and potential difference

Resistance and Resistivity

Topic overview Resistance and Ohm's law Ohmic and non-ohmic behaviour Resistors in series and in parallel Investigating current, voltage and resistance in series and parallel circuits Electrical power and energy in resistive circuits Resistivity and the equation R = ρl/A Measuring the resistivity of a metal Current–voltage characteristics of a conductor, a lamp and a diode Resistance, temperature and superconductivity

Internal Resistance and Potential Dividers

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Waves

Topic overview Transverse and longitudinal waves Amplitude, period, frequency and wavelength Phase and phase difference Reading wave graphs The wave equation Polarisation The electromagnetic spectrum

Refraction

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Quantum Physics

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Wave-Particle Duality

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Astronomy

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Practical Skills and Data Analysis

Topic overview Choosing and using measuring instruments Precision, accuracy and recording measurements Using the cathode ray oscilloscope to measure voltage and frequency Tables, graphs and presenting results Linearising a relationship and using the gradient Absolute and percentage uncertainty Combining uncertainties and uncertainty on a graph Random and systematic error, reliability and refining an experiment

Deformation of Solids

Topic overview Hooke's law and the spring constant Elastic and plastic deformation and the elastic limit Stress, strain and the Young modulus Measuring the Young modulus of a wire Strain energy and force–extension graphs Choosing materials: strength, stiffness and cost

Thermal Physics

Topic overview Boyle's law, Charles's law and the pressure law The ideal gas equation pV = nRT The Avogadro constant, the mole and pV = NkT Internal energy and the distribution of molecular energy The kinetic theory equation pV = ⅓Nm⟨c²⟩Average molecular kinetic energy and temperature Absolute zero and the kelvin scale Specific heat capacity and the electrical method

Uniform Circular Motion

Topic overview Angular velocity, period and frequency Linear speed and angular velocity: v = rω Centripetal acceleration and centripetal force Applying F = mv²/r to motion at constant speed

Simple Harmonic Motion

Topic overview Defining simple harmonic motion and a = −ω²x Displacement, velocity and acceleration: x = A cos ωt The simple pendulum and T = 2π√(l/g)The loaded spiral spring and T = 2π√(m/k)SHM graphs and finding velocity from a gradient Free vibrations, forced vibrations and resonance Damping: light, critical and over-damping

The Nucleus and Radioactive Decay

Topic overview Alpha-particle scattering and the nuclear atom Nuclear radius and nucleon number The density of nuclear matter Alpha, beta and gamma radiation: nature, penetration and range Nuclear equations and changes in nucleon and proton number The random and exponential nature of radioactive decay Activity, the decay constant and A = −λN Exponential decay calculations with A = A₀e^(−λt)Half-life and measuring it

Nuclear Energy, Fission and Fusion

Topic overview Mass–energy equivalence and E = Δmc² Mass defect and binding energy The binding energy per nucleon curve Inside a fission reactor Nuclear power: social, environmental, security and economic issues The ITER tokamak fusion reactor Plasma confinement: gravitational, inertial and magnetic

Gravitational Fields

Topic overview Fields of force and field lines Gravitational field strength Newton's law of universal gravitation The field strength of a point mass Circular motion of planets and satellites Kepler's third law Geostationary satellites

Electric Fields

Topic overview Electric field strength Coulomb's law The field of a point charge Uniform fields between parallel plates Comparing gravitational and electric fields Field strength calculations and combined fields

Capacitors

Topic overview Capacitance and the farad Energy stored in a charged capacitor Capacitors in series and in parallel Charging and discharging a capacitor The exponential decay equations The time constant Flash guns and defibrillators Uses of capacitors in circuits Capacitor calculations and graph work

Magnetic Fields

Topic overview Magnetic fields around currents The force on a current-carrying conductor Magnetic flux density The electric motor Magnetic flux and flux linkage Faraday's law of electromagnetic induction Lenz's law The alternating current generator Transformers Power losses and high-voltage transmission

Charged Particles and Accelerators

Topic overview Charged particles in a uniform electric field Charged particles in a magnetic field Circular paths in a magnetic field Comparing electric and magnetic deflection The synchrotron Relativistic mass increase Antimatter and annihilation

Fundamental Particles

Topic overview Fundamental particles The four fundamental forces Classifying particles Quarks and the structure of hadrons Conservation laws Beta decay in the quark model

Linear Motion and Dynamics

The equations of motion for uniform acceleration

3 things to know
Unit AS 1

Overview

Recall questions on the four suvat equations and when they may be used, choosing the right one when time or final velocity is unknown, the sign convention for vertical motion, worked problems on a car accelerating and braking and a stone dropped or thrown upwards, and why a journey in stages cannot be done in one step.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Explain how the equation s = ½(u + v)t follows from the definition of average velocity.

Key term

Explain the sign convention that must be applied when using the equations of motion.

Numbers

A stone is dropped from rest and falls 45 m. Calculate its speed on landing, taking g as 9.81 m s⁻².

Questions from this subtopic

Each one with the model answer underneath.

1
State the four equations of motion for uniform acceleration, defining each symbol and its unit.
Model answer
The equations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t, where u is the initial velocity in m s⁻¹, v the final velocity in m s⁻¹, a the uniform acceleration in m s⁻², t the time in seconds and s the displacement in metres.
2
State the conditions under which the equations of motion may be used.
Model answer
They apply only when the acceleration is constant in both size and direction, so the motion must be in a straight line with uniform acceleration throughout the interval considered.
3
Which equation of motion should be chosen when the time taken is neither known nor required?
Model answer
The equation v² = u² + 2as should be used, because it links initial velocity, final velocity, acceleration and displacement without involving time.
4
Which equation of motion should be chosen when the final velocity is neither known nor required?
Model answer
The equation s = ut + ½at² should be used, because it links displacement to initial velocity, acceleration and time without involving the final velocity.
5
Explain how the equation s = ½(u + v)t follows from the definition of average velocity.
Model answer
When the acceleration is uniform the average velocity is simply the mean of the initial and final velocities, ½(u + v), and displacement is average velocity multiplied by time.
6
Explain the sign convention that must be applied when using the equations of motion.
Model answer
One direction along the line of motion is chosen as positive at the start, and every displacement, velocity and acceleration acting in the opposite direction is then entered into the equations as a negative number.

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