Kinematics: Describing Motion

Formulas (3)

• Distance and displacement, speed and velocity · Average speed and average velocity
  $$\text{average speed} = \frac{\text{distance}}{t} \qquad \bar{v} = \frac{\Delta s}{t}$$
• Relative velocity and Galilean transformations · Relative velocity
  $$v_{AB} = v_A - v_B \qquad t_{\text{catch}} = \frac{\text{gap}}{v_A - v_B}$$
• Acceleration: the rate of change of velocity · Average acceleration
  $$a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}$$

Watch out for (5)

• Average speed is not the average of the speeds
  → Distance and displacement, speed and velocity
• Average velocity uses the straight-line displacement
  → Distance and displacement, speed and velocity
• Galilean transformations need uniform straight-line relative motion
  → Relative velocity and Galilean transformations
• Check the units before comparing a gap with a speed
  → Relative velocity and Galilean transformations
• Zero velocity does not mean zero acceleration
  → Acceleration: the rate of change of velocity

Formulas (3)

• The equations of motion for constant acceleration · Equations of uniformly accelerated motion
  $$v = u + at \qquad s = ut + \tfrac{1}{2}at^2 \qquad v^2 = u^2 + 2as$$
• Motion graphs: gradients and areas · Reading a v-t graph
  $$a = \text{gradient} = \frac{\Delta v}{\Delta t} \qquad s = \text{area under the line}$$
• Free fall and vertical throws · Falling from rest and the highest point of a throw
  $$h = \tfrac{1}{2}gt^2, \quad v = gt \qquad h_{\max} = \frac{u^2}{2g}$$

Watch out for (4)

• Stopping distance grows with the square of the speed
  → The equations of motion for constant acceleration
• The equations hold only while the acceleration is constant
  → The equations of motion for constant acceleration
• The same flat line means different things on different graphs
  → Motion graphs: gradients and areas
• Heavier objects do not fall faster
  → Free fall and vertical throws

Formulas (3)

• Projectile motion: horizontal and vertical parts are independent · Launch from level ground
  $$t_{\text{flight}} = \frac{2u_y}{g} \qquad R = u_x\, t_{\text{flight}}$$
• Period, frequency and angular velocity in circular motion · Circular motion quantities
  $$f = \frac{1}{T} \qquad \omega = \frac{2\pi}{T} = 2\pi f \qquad v = \omega r$$
• Centripetal acceleration: always towards the centre · Centripetal acceleration
  $$a = \frac{v^2}{r} = \omega^2 r$$

Watch out for (3)

• At the top of its path a projectile is still moving
  → Projectile motion: horizontal and vertical parts are independent
• Change rpm into hertz before using 2π
  → Period, frequency and angular velocity in circular motion
• Constant speed in a circle still means acceleration
  → Centripetal acceleration: always towards the centre