Kinematics flashcards

Kinematics

Introduction

• Will a Tesla beat a sports car?
• Watch from the 1min 26sec mark onwards.

Distance and Displacement

• Distance:
  • Only the magnitude is important; hence distance is a scalar.
  • SI unit: metre (m)
• Displacement:
  • Both magnitude and direction are important.
  • SI unit: metre (m)

Examples of Distance and Displacement

• Example 1:
  • 5 steps right, then 5 steps left.
  • Distance = 10 steps; Displacement = 0 steps.
• Example 2:
  • Car travels 8 km East then U-turn, travels 5 km West.
  • Distance = 8 + 5 = 13 km; Displacement = 8 - 5 = 3 km (East).

Speed

• Definition: Speed = distance moved per unit time.
• Formula: v = \frac{d}{t} where:
  • d = distance travelled (m)
  • t = time taken (s)
  • SI unit: metre per second (m/s)

Average Speed

• Average Speed = total Distance / total time.

Examples of Average Speed

• Worked Example: A car driver takes 2 hours for a 75 km journey with a break.
  • Average Speed = \frac{75}{2 - 0.5 - 0.25} = 60 ext{ km/h}

Velocity

• Definition: Rate of change of displacement.
• Formula: v = \frac{d}{t}
• Characteristics:
  • Changes with magnitude, direction, or both.

Difference between Speed and Velocity

• Speed:
  • Scalar, independent of direction; always positive.
• Velocity:
  • Vector, depends on direction; can be negative.

Examples of Velocity

• A car drives 20 km East, then 15 km West.
  • Average Speed = \frac{20 + 15}{\frac{20}{60}} = 105 ext{ km/h}
  • Average Velocity = \frac{5}{\frac{20}{60}} = 15 ext{ km/h East}

Acceleration

• Definition: Rate of change of velocity.
• Formula: a = \frac{v - u}{t} where:
  • a = acceleration (m/s²)
  • u = initial velocity (m/s)
  • v = final velocity (m/s)
  • t = time (s)
• SI unit: metre per second squared (m/s²)

Worked Examples of Acceleration

• Racing car accelerates from 5 m/s to 13 m/s in 4 s.
  • a = \frac{13 - 5}{4} = 2 ext{ m/s²}
• A ball released from rest falls under gravity, accelerating at 10 ext{ m/s²}.

Deceleration

• Term for negative acceleration, also called retardation.
• Example: A Ferrari goes from 30 m/s to halt in 5 s.
  • a = \frac{0 - 30}{5} = -6 ext{ m/s²}

Graphs in Kinematics

• Distance-Time Graphs:

  • Vertical = distance, horizontal = time.
  • Gradients calculate speed; the area under the curve represents displacement.
  • Different shapes indicate uniform and non-uniform motion.

• Speed-Time Graphs:

  • Vertical = speed, horizontal = time.
  • Gradients indicate acceleration; area under the graph gives distance traveled.

Acceleration of Free Fall

• Objects fall due to gravity with acceleration approx. 10 ext{ m/s²} regardless of mass if air resistance is negligible.

Quick Checks

• 1. Acceleration is the rate of change of velocity.
• 2. SI unit of acceleration is m/s².
• 3. Formula for acceleration: a = \frac{v - u}{t} .
• 4. Negative acceleration is known as deceleration.

Applications

• Average Speed Example: A car takes 60 minutes for 100 km, and 30 minutes for 20 km.
• Speed-Time Graph Applications: Determine acceleration, distance traveled, etc.
• Analyzing athletes’ speeds or vehicles’ speeds through various sections of motion.