A-Level Maths OCR B (MEI) H640

Understand and use the language of kinematics.

Position, displacement, distance travelled; speed, velocity; acceleration, magnitude of acceleration; relative velocity (in 1-dimension).

Average speed $=$ distance travelled $÷$ elapsed time

Average velocity $=$ overall displacement $÷$ elapsed time

Know the difference between position, displacement, distance and distance travelled.

Know the difference between velocity and speed, and between acceleration and magnitude of acceleration.

Be able to draw and interpret kinematics graphs for motion in a straight line, knowing the significance (where appropriate) of their gradients and the areas underneath them.

Position-time, displacement-time, distance-time, velocity-time, speed-time, acceleration-time.

Be able to differentiate position and velocity with respect to time and know what measures result.

Notation:

• $v = \dfrac{dr}{dt}$, $a = \dfrac{dv}{dt} = \dfrac{d^2r}{dt^2}$

Be able to integrate acceleration and velocity with respect to time and know what measures result.

Notation:

• $r = \displaystyle\int{v}~dt$, $v = \displaystyle\int{a}~dt$

Be able to recognise when the use of constant acceleration formulae is appropriate.

Learners should be able to derive the formulae.

Notation:

• $s = \frac{1}{2}(u+v)t$
• $s = vt - \frac{1}{2}at^2$
• $v = u + at$
• $s = ut + \frac{1}{2}at^2$
• $v^2 = u^2 + 2as$

Be able to solve kinematics problems using constant acceleration formulae and calculus for motion in a straight line.