#3.02a
Understand and be able to use the language of kinematics: position, displacement, distance, distance travelled, velocity, speed, acceleration, equation of motion.
Learners should understand the vector nature of displacement, velocity and acceleration and the scalar nature of distance travelled and speed.
#3.02b
Understand, use and interpret graphs in kinematics for motion in a straight line.
Interpret graphs in kinematics for motion in a straight line
#3.02c
Be able to interpret displacement-time and velocity-time graphs, and in particular understand and be able to use the facts that the gradient of a displacement-time graph represents the velocity, the gradient of a velocity-time graph represents the acceleration, and the area between the graph and the time axis for a velocity-time graph represents the displacement.
Interpret graphs in kinematics for motion in a straight line
#3.02d
Understand, use and derive the formulae for constant acceleration for motion in a straight line:
\(v = u + at\)
\(s = ut + \frac{1}{2}at^2\)
\(s = \frac{1}{2}(u+v)t\)
\(v^2 = u^2 + 2as\)
\(s = vt - \frac{1}{2}at^2\)
Learners may be required to derive the constant acceleration formulae using a variety of techniques:
1. b y integration, e.g. \(v = \int{a}~dt \implies v = u + at\),
2. by using and interpreting appropriate graphs, e.g. velocity against time,
3. by substitution of one (given) formula into another (given) formula, e.g. substituting \(v = u + at\) into \(s = \frac{1}{2}(u+v)t\) to obtain \(s = ut + \frac{1}{2}at^2\).
#3.02e
Be able to extend the constant acceleration formulae to motion in two dimensions using vectors:
\(\bold{v} = \bold{u} + \bold{a}t\)
\(\bold{s} = \bold{u}t + \frac{1}{2}\bold{a}t^2\)
\(\bold{s} = \frac{1}{2}(\bold{u}+\bold{v})t\)
\(\bold{s} = \bold{v}t - \frac{1}{2}\bold{a}t^2\)
Questions set involving vectors may involve either column vector notation, e.g. \(\bold{u} = \begin{pmatrix} u_1 \\ u_2 \end{pmatrix}\) or \(\bold{i}\), \(\bold{j}\) notation, e.g. \(\bold{u} = u_1\bold{i} + u_2\bold{j}\).
[The formula \(\bold{v}⋅\bold{v} = \bold{u}⋅\bold{u} + 2\bold{a}⋅\bold{s}\) is excluded.]
#3.02f
Be able to use differentiation and integration with respect to time in one dimension to solve simple problems concerning the displacement, velocity and acceleration of a particle:
\(v = \dfrac{ds}{dt}\)
\(a = \dfrac{dv}{dt} = \dfrac{d^2s}{dt^2}\)
\(s = \displaystyle\int{v}~dt\) and \(v = \displaystyle\int{a}~dt\)
#3.02g
Be able to extend the application of differentiation and integration to two dimensions using vectors:
\(\bold{x} = f(t)\bold{i} + g(t)\bold{j}\)
\(\bold{v} = \dfrac{d\bold{x}}{dt} = \dot{\bold{x}} = f'(t)\bold{i} + g'(t)\bold{j}\)
\(\bold{a} = \dfrac{d\bold{v}}{dt} = \dot{\bold{v}} = f''(t)\bold{i} + g''(t)\bold{j}\)
\(\bold{x} = \displaystyle\int{\bold{v}}~dt\) and \(\bold{v} = \displaystyle\int{\bold{a}}~dt\)
Questions set may involve either column vector or \(\bold{i}\), \(\bold{j}\) notation.
#3.02h
Be able to model motion under gravity in a vertical plane using vectors where \(\bold{a} = \begin{pmatrix} 0 \\ -g \end{pmatrix}\) or \(\bold{a} = -g\bold{j}\).
Model motion under gravity in a vertical plane using vectors
#3.02i
Be able to model the motion of a projectile as a particle moving with constant acceleration and understand the limitation of this model.
Includes being able to:
1. Use horizontal and vertical equations of motion to solve problems on the motion of projectiles.
2. Find the magnitude and direction of the velocity at a given time or position.
3. Find the range on a horizontal plane and the greatest height achieved.
4. Derive and use the cartesian equation of the trajectory of a projectile.
[Projectiles on an inclined plane and problems with resistive forces are excluded.]