Mechanics

The Mechanics element of the AS-Level in Mathematics consists of the following topic areas:
Quantities & Units in Mechanics, Kinematics and Forces & Newton’s Laws. In addition to these topics, the A-Level in Mathematics also covers Moments. See bottom of the page for things you should memorise for AS Mechanics.

Quantities & Units in AS-Level Maths:

understand the quantities and units of length, time, mass, velocity, acceleration, force, weight…

Quantities & Units in A-Level Maths:

In addition to the above:

(no additional content)

Kinematics in AS-Level Maths:

understand position, displacement, distance, velocity, speed and acceleration
understand and interpret graphs for motion on a straight line
understand, use and derive the SUVAT equations
use calculus in kinematics for motion on a straight line

Kinematics in A-Level Maths:

In addition to the above (including extension to two dimensions in some areas):

projectile motion under gravity

Forces & Newton’s Laws in AS-Level Maths:

normal reaction, tension, thrust or compression, resistance and Newton’s first law
Newton’s second law for motion on a straight line
using weight under gravity
Newton’s third law, forces in equilibrium, pulleys & connected particles

Forces & Newton’s Laws in A-Level Maths:

In addition to the above (where resolution in two dimensions is also required) the following topics are covered:

resultant forces and dynamics
friction

Moments in AS-Level Maths:

Not covered in AS-Level Maths

Moments in A-Level Maths:

In addition to the above:

using moments in problems with static rigid bodies in equilibrium

Things to remember for AS Mechanics

The SUVAT Equations

$\hspace{10pt}V=U+AT$
$\hspace{10pt}S=\left(\frac{U+V}{2}\right)T$
$\hspace{10pt}V^2=U^2+2AS$
$\hspace{10pt}S=UT+\frac{1}{2}AT^2$
$\hspace{10pt}S=VT-\frac{1}{2}AT^2$

Go to the SUVAT Equations page

Variable Acceleration

${\bf v}=\frac{d{\bf r}}{dt}$
${\bf a}=\frac{d{\bf v}}{dt}=\frac{d^2{\bf r}}{dt^2}$
${\bf v}=\int{\bf a}dt$
${\bf r}=\int{\bf v}dt=\int\left(\int{\bf a}dt\right)dt$

Go to Variable Acceleration page.

Other

Gravity: $g=9.8m/s^2$
Resultant Force: $F=ma$
Friction: $F\leq \mu R$ , at maximum when object is moving or about to move.