Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration.

Students should know that distance and speed must be positive.

Terms and definitions

Understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph.

Graphical solutions to problems may be required.

Interpret graphs in kinematics for motion in a straight line

Understand, use and derive the formulae for constant acceleration for motion in a straight line.

Extend to 2 dimensions using vectors.

Derivation may use knowledge of sections 7.2 and/or 7.4.

Understand and use suvat formulae for constant acceleration in 2-D,

e.g. \(\bold{v} = \bold{u} + \bold{a}t\), \(\bold{r} = \bold{u}t + \frac{1}{2}\bold{a}t^2\) with vectors given in \(\bold{i} - \bold{j}\) or column vector form.

Use vectors to solve problems.

Acceleration in a straight line Acceleration using vectors

Use calculus in kinematics for motion in a straight line:

\(v = \dfrac{dr}{dt}\), \(a = \dfrac{dv}{dt} = \dfrac{d^2r}{dt^2}\), \(r = \displaystyle\int{v}~dt\), \(v = \displaystyle\int{a}~dt\)

The level of calculus required will be consistent with that in Sections 7 and 8 in Paper 1 and Sections 6 and 7 in Paper 2.

Extend to 2 dimensions using vectors.

Differentiation and integration of a vector with respect to time. e.g.
Given \(\bold{r} = t^2\bold{i} + t^{\frac{3}{2}}\bold{j}\) , find \(\dot{r}\) and \(\ddot{r}\) at a given time.

Use calculus in kinematics for motion in a straight line Use calculus in kinematics for vectors

Model motion under gravity in a vertical plane using vectors; projectiles.

Derivation of formulae for time of flight, range and greatest height and the derivation of the equation of the path of a projectile may be required.

Model motion under gravity in a vertical plane using vectors Projectiles