Kinematics and Motion — NDA Physics

Formulas (3)

• Distance vs displacement · Distance and displacement
  $$|\vec{s}| \leq d \qquad \vec{s}_{\text{round trip}} = 0$$
• Speed, velocity, and their averages · Average speed and velocity
  $$\bar{v}_{\text{speed}} = \dfrac{d}{t} \qquad \bar{v}_{\text{velocity}} = \dfrac{\vec{s}}{t}$$
• Position vector r(t) and net displacement · Position vector and its derivatives
  $$\vec{v} = \dfrac{d\vec{r}}{dt}, \quad \vec{a} = \dfrac{d\vec{v}}{dt}, \quad |\vec{s}_{\text{net}}| = \sqrt{s_x^2 + s_y^2}$$

Reference tables (1)

Watch out for (5)

• Speed is the scalar; velocity is the vector
  → Scalars vs vectors
• Round trip: distance is non-zero, displacement is zero
  → Distance vs displacement
• Average speed is NOT |average velocity| in general
  → Speed, velocity, and their averages
• Add perpendicular legs as vectors, not as numbers
  → Position vector r(t) and net displacement
• Force ∥ momentum needs both vectors checked
  → Position vector r(t) and net displacement

Formulas (5)

• Acceleration — rate of change of velocity · Acceleration
  $$a = \dfrac{v - u}{t}$$
• The three equations of motion · Equations of motion (constant a)
  $$v = u + at \qquad s = ut + \tfrac{1}{2}at^2 \qquad v^2 = u^2 + 2as$$
• Distance covered in the nth second · Distance in the nth second
  $$s_n = u + \tfrac{1}{2}a(2n - 1)$$
• Reading a velocity-time graph · Velocity-time graph readings
  $$a = \text{slope} = \dfrac{\Delta v}{\Delta t}, \qquad s = \text{area under the graph}$$
• Reading a position-time graph · Position-time slope
  $$v = \dfrac{dx}{dt} = \text{slope of the } x\text{-}t \text{ graph}$$

Watch out for (7)

• Deceleration is negative acceleration, not 'no' acceleration
  → Acceleration — rate of change of velocity
• v² − u² = 2as, with the right sign
  → The three equations of motion
• These equations need CONSTANT acceleration
  → The three equations of motion
• The nth-second distance is not the total distance
  → Distance covered in the nth second
• Slope is acceleration; AREA is displacement — don't swap them
  → Reading a velocity-time graph
• Check which axis is which before reading the slope
  → Reading a position-time graph
• Quadratic, not linear, distance growth
  → Interpreting motion: shapes and statements

Formulas (2)

• Vertical throw — straight up under gravity · Vertical throw (up positive, a = −g)
  $$v = u - gt, \qquad h_{\max} = \dfrac{u^2}{2g}, \qquad t_{\text{up}} = \dfrac{u}{g}$$
• Horizontal projectile — independence of motions · Horizontal projectile
  $$t = \sqrt{\dfrac{2h}{g}}, \qquad R = u\,t$$

Watch out for (2)

• Velocity is zero at the top, acceleration is NOT
  → Vertical throw — straight up under gravity
• Horizontal speed never affects the fall time
  → Horizontal projectile — independence of motions

Formulas (2)

• Centripetal acceleration — v²/r toward the centre · Centripetal acceleration
  $$a_c = \dfrac{v^2}{r}$$
• Average acceleration over part of a circle · Average acceleration over half a circle
  $$\bar{a} = \dfrac{|\Delta \vec{v}|}{\Delta t} = \dfrac{2v}{\pi r / v} = \dfrac{2v^2}{\pi r}$$

Watch out for (3)

• Constant speed is not constant velocity
  → Uniform circular motion — constant speed, changing velocity
• Centripetal acceleration does not change the speed
  → Centripetal acceleration — v²/r toward the centre
• Average acceleration is not the instantaneous v²/r
  → Average acceleration over part of a circle