Kinematics: CDS Physics

Formulas (2)

• Distance, displacement and average speed · Average speed
  $$\bar{v} = \dfrac{\text{total distance}}{\text{total time}} \qquad \bar{v}_{\text{equal distances}} = \dfrac{2v_1v_2}{v_1 + v_2} \qquad \bar{v}_{\text{equal times}} = \dfrac{v_1 + v_2}{2}$$
• Equations of motion for uniform acceleration · Equations of motion
  $$v = u + at \qquad s = ut + \tfrac{1}{2}at^{2} \qquad v^{2} = u^{2} + 2as \qquad s = \dfrac{u + v}{2}\,t \qquad s_n = u + \dfrac{a}{2}(2n - 1)$$

Reference tables (1)

Watch out for (8)

• Half a lap gives the diameter, not half the circumference
  → Distance, displacement and average speed
• Average speed over equal distances is not the plain average
  → Distance, displacement and average speed
• Count whole laps first
  → Distance, displacement and average speed
• Change minutes into hours before dividing
  → Equations of motion for uniform acceleration
• The n-th second is one second, not n seconds
  → Equations of motion for uniform acceleration
• Retardation enters with a minus sign
  → Equations of motion for uniform acceleration
• Flat on one graph is not flat on the other
  → Reading motion graphs
• Area gives displacement, not average velocity
  → Reading motion graphs

Formulas (3)

• Adding vectors and resolving them · Resultant of two vectors
  $$R = \sqrt{A^{2} + B^{2} + 2AB\cos\theta} \qquad |A - B| \le R \le A + B \qquad \vec{v} = \dfrac{d\vec{r}}{dt}, \ \vec{a} = \dfrac{d\vec{v}}{dt}$$
• Free fall and horizontal launch · Free fall and horizontal launch
  $$h = \tfrac{1}{2}gt^{2} \qquad t = \sqrt{\dfrac{2h}{g}} \qquad v = \sqrt{2gh} \qquad R = u\sqrt{\dfrac{2h}{g}}$$
• Uniform circular motion · Centripetal acceleration
  $$a = \dfrac{v^{2}}{r} = \omega^{2}r \qquad v = \omega r \qquad T = \dfrac{2\pi r}{v}$$

Watch out for (7)

• Sizes add only when the directions match
  → Adding vectors and resolving them
• Combine forces along one line first
  → Adding vectors and resolving them
• sin and cos swap with the angle you measure from
  → Adding vectors and resolving them
• The launch speed does not change the time in the air
  → Free fall and horizontal launch
• Acceleration stays constant, speed does not
  → Free fall and horizontal launch
• Uniform circular motion is accelerated
  → Uniform circular motion
• Constant size is not constant acceleration
  → Uniform circular motion