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Motion and Forces

Subject: Physics
Topic: 1
Cambridge Code: 0625 / 0972 / 5054

Kinematics​

Key Quantities​

Distance - Total path length (scalar) Displacement - Straight line from start to end (vector)

Speed - Rate of change of distance (scalar) v=distancetimev = \frac{\text{distance}}{\text{time}}

Velocity - Rate of change of displacement (vector) v=displacementtimev = \frac{\text{displacement}}{\text{time}}

Acceleration - Rate of change of velocity a=change in velocitytime=ΔvΔta = \frac{\text{change in velocity}}{\text{time}} = \frac{\Delta v}{\Delta t}

Equations of Motion​

For constant acceleration:

v=u+atv = u + at

s=ut+12at2s = ut + \frac{1}{2}at^2

v2=u2+2asv^2 = u^2 + 2as

where:

  • uu = initial velocity
  • vv = final velocity
  • aa = acceleration
  • tt = time
  • ss = displacement

Example​

Object accelerates from 5 m/s to 15 m/s in 4 seconds Find acceleration: a=15−54=2.5 m/s2a = \frac{15 - 5}{4} = 2.5 \text{ m/s}^2

Forces​

Force - Push or pull that changes motion or shape

Newton (N) - Unit of force (kg·m/s²)

Newton's First Law​

Body at rest stays at rest; body in motion stays in motion, unless acted upon by unbalanced force

Inertia - Tendency to resist change in motion

Newton's Second Law​

F=maF = ma

Force = mass × acceleration

Newton's Third Law​

For every action, there is an equal and opposite reaction

Example: When you jump, you push down on Earth; Earth pushes up on you equally

Types of Forces​

Weight: W=mgW = mg (force of gravity on mass)

Friction: Opposes motion

  • Static friction: Prevents motion
  • Kinetic friction: Opposes moving objects
  • Ff=μNF_f = \mu N (friction force = coefficient × normal force)

Normal Force: Force perpendicular to surface

Tension: Force in rope or string

Air Resistance: Opposes motion through air

Momentum​

Momentum - Product of mass and velocity

p=mvp = mv

Units: kg·m/s or N·s

Conservation of Momentum​

In isolated system, total momentum before = total momentum after

pbefore=pafterp_{\text{before}} = p_{\text{after}}

m1u1+m2u2=m1v1+m2v2m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

Impulse​

Impulse - Change in momentum

Impulse=F×t=Δp\text{Impulse} = F \times t = \Delta p

Work, Energy, Power​

Work: W=F×dW = F \times d (Force × distance in direction of force)

Energy: Capacity to do work

Kinetic Energy: Ek=12mv2E_k = \frac{1}{2}mv^2

Potential Energy: Ep=mghE_p = mgh

Power: P=WtP = \frac{W}{t} (Work per unit time)

Circular Motion (Brief)​

In circular motion at constant speed:

  • Velocity is constant magnitude but changes direction
  • Acceleration directed toward center (centripetal)
  • Force required: F=mv2rF = \frac{mv^2}{r}

Key Points​

  1. Distinguish distance/displacement, speed/velocity
  2. Use equations of motion for constant acceleration
  3. F = ma (Newton's 2nd law)
  4. Action-reaction pairs (Newton's 3rd law)
  5. Momentum conservation in collisions
  6. Work = Force × distance

Practice Questions​

  1. Calculate acceleration from velocity change
  2. Use equations of motion to find unknowns
  3. Apply F = ma to solve force problems
  4. Use momentum conservation in collisions
  5. Calculate work done and power
  6. Draw free body diagrams

Revision Tips​

  • Learn the three equations of motion
  • Understand vector vs. scalar quantities
  • Practice free body diagrams
  • Momentum conservation in collisions
  • Master energy equations
  • Distinguish between force types