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Most Important And Most Frequently Used Formulas in Physics (1)

Physics Problem Solving For High School - Formula, Definition and explanations  - Some of the most important and most frequently used formulas in physics lessons at our school are presented and explained below. We look forward to helping you solve physics problems in school.
The Most Important And Most Frequently Used Formulas in Physics (1)
A. Relative Velocity
Formula, Definition and explanations
\[v_{AC} = v_{AB}+v_{BC}\]
  • $v_{AC}$ is the velocity of A with respect to C (vector)
  • $v_{AB}$ is the velocity of A with respect to B (vector)
  • $v_{BC}$ is the velocity of B with respect to C (vector)
B. Kinematics 
Formula, Definition and explanations
\[v_{ix} = |v_i|\cos(\theta) \\ v_{iy} = |v_i|\sin(\theta)\]
  • $v_i$ is the initial velocity (vector)
  • $v_{ix}$ is the component of the initial velocity along the horizontal direction x (scalar)
  • $v_{iy}$ is the component of the initial velocity along the vertical direction y (scalar)
  • $\theta $ is the initial angle that vi makes with the horizontal.
\[\Delta x = |v_i|\cos(\theta) \Delta t\]
  • $\Delta x$ is the displacement along the horizontal direction x
\[\Delta y = |v_i|\sin(\theta) \Delta t - \dfrac{1}{2} g (\Delta t)^2\]
  • $\Delta y$ is the displacement along the vertical direction y
\[R = \dfrac{v^2_i \sin(2\theta)}{g}\]
  • R is the range or horizontal distance travelled when the projectile hits the ground
\[T = \dfrac{2 v_i \sin(\theta)}{g}\]
  • T is total time to hit the ground
\[H = \dfrac{v^2_i \sin^2(\theta)}{2 g}\]
  • H maximum height reached above the ground
g = 9.8 m.s2

C. Kinematics
Formula, definition and explanations
\[s_{av} = \dfrac{d}{\Delta t}\] $s_{av}
  • $ is the average speed (scalar)
  • d is the distance
  • Δt is the time elapsed
\[v_{av} = \dfrac{x_f - x_i}{t_f - t_i} =\dfrac{\Delta x}{\Delta t}\]
  • $v_{av}$ is the average velocity (vector)
  • Δx is the displacement(vector)
  • Δt is the time elapsed
\[a_{av} = \dfrac{v_f - v_i}{t_f - t_i} =\dfrac{\Delta v}{\Delta t}\]
  • $a_{av}$ is the average acceleartion (vector)
  • Δv is the change in velocity (vector)
  • Δt is the time elapsed
\[v_{av} = \dfrac{v_i + v_f}{2}\]
  • $v_{av}$ is the average velocity (vector)
  • $v_i$ is the initial velocity (vector)
  • $v_f$ is the final velocity (vector)
\[v_{f} = v_{i} + a \Delta t\]
  • $v_f$ is the final velocity (vector)
  • $v_i$ is the initial velocity (vector)
  • a is the acceleration (vector)
\[\Delta x = v_i \Delta t + \dfrac{1}{2} a (\Delta t)^2\]
  • Δx is the displacement (vector)
  • vi is the initial velocity (vector)
  • a is the acceleration (vector)
\[\Delta x = v_f \Delta t - \dfrac{1}{2} a (\Delta t)^2\]
  • Δx is the displacement (vector)
  • $v_f$ is the final velocity (vector)
  • a is the acceleration (vector)
\[\Delta x = \dfrac{v_f+v_i}{2} \Delta t\]
  • Δx is the displacement (vector)
  • vf is the final velocity (vector)
  • vi is the initial velocity (vector)
\[v^2_f = v^2_i + 2 a \cdot \Delta x\]
  • $v_f $is the final velocity (vector)
  • vi is the initial velocity (vector)
  • Δx is the displacement (vector)
  • a is the acceleration (vector)
D. Dynamics (Forces and Momentum)
Formula, Definition and explanations
\[F = m a\]
  • F is the net force (vector)
  • m is the mass
  • a is the acceleration (vector)
\[F_g = m g\]
  • Fg is the weight (vector)
  • m is the mass
  • g is the acceleration (near the Earth) due to gravitation (vector)
\[| F_f | = \mu | F_N |\]
  • Ff is the force of friction (vector)
  • μ is the coefficient of friction (μ may be μk kinetic coefficient or μs static coefficient of friction)
  • FN is the normal (to the surface) force (vector)
\[p = m v\]
  • p is the momentum (vector)
  • m is the mass
  • v is the velocity (vector)
\[\Delta p = F \Delta t\]
  • Δp is the change in momentum (vector)
  • F is the applied force (vector)
  • Δt is the elapsed time
  • (F Δt) is called impulse (vector)

E. Circular Motion
Formula, Definition and explanations
\[a_c = \dfrac{v^2}{r}\]
  • ac is the centripetal acceleration
  • v is the velocity
  • r is the radius
\[F_c = \dfrac{m v^2}{r}\]
  • Fc is the centripetal force
  • v is the velocity
  • m is the mass
  • r is the radius
\[v = \dfrac{2 \pi r}{T}\]
  • v is the velocity
  • r is the radius
  • T is the period (time for one complete revolution)
F. Work, Potential and Kinetic Energies
Formula, Definition and explanations
\[W = F d \cos \theta\]
  • W is the work done by the force F
  • F is the applied force (constant)
  • d is the distance
  • θ is the angle between F and the direction of motion
\[E_k = \dfrac{1}{2} m v^2\]
  • Ek is the kinetic energy
  • v is the velocity
  • m is the mass
\[E_p = m g h\]
  • Ep is the potential energy of an object close to the surface of Earth
  • m is the mass of the object
  • h is the height of the object with respect to some refernce (ground for example)
  • g = 9.8 m/s2
\[E_t = E_k + E_p\]
  • Et is the total energy
  • Ek is the kinetic energy
  • Ep is the potential energy
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Most Important And Most Frequently Used Formulas in Physics (2)