Physics: Velocity and Acceleration

Overview

This lecture explains the differences between velocity and acceleration, introduces key formulas, and provides examples of calculating average and instantaneous acceleration.

Velocity vs. Speed

• Velocity is a vector showing how fast displacement (change in position) occurs per unit time.
• Average velocity = (final position – initial position) / elapsed time.
• Instantaneous velocity is found using the same formula as average velocity as the time interval approaches zero.
• Speed measures how fast distance changes; velocity measures how fast displacement changes and includes direction.
• Example: A car moving at 30 m/hr east has a velocity of 30 m/hr east.

Introduction to Acceleration

• Acceleration shows how fast velocity changes per unit of time.
• Average acceleration = (final velocity – initial velocity) / elapsed time.
• Instantaneous acceleration is calculated as the time interval approaches zero.
• Example: An acceleration of 8 m/s² means each second, velocity increases by 8 m/s.

Key Acceleration Formula

• For constant acceleration: final velocity = initial velocity + (acceleration × time).
• This formula is valid only if acceleration is constant.

Example Problems

• Problem 1: Car accelerates from 15 m/s to 45 m/s in 5 seconds.
  • a = (45 – 15) / 5 = 6 m/s².
• Problem 2: Truck accelerates from 25 km/h to 45 km/h in 40 s.
  • a = (45 – 25) / 40 = 0.5 km/h/s.
  • Convert to m/s²: 0.5 × 1000 / (60 × 60) ≈ 0.139 m/s².
• Problem 3: Car accelerates from rest at 3.5 m/s² for 12 sec.
  • Final speed = 0 + (3.5 × 12) = 42 m/s.
• Problem 4: Bus accelerates from 12 m/s at 1.2 m/s² for 15 s.
  • Final speed = 12 + (1.2 × 15) = 30 m/s.
• Problem 5: Car decelerates from 95 mph to rest in 4 sec.
  • Convert 95 mph to m/s: ≈ 42.4 m/s.
  • a = (0 – 42.4) / 4 = –10.6 m/s² (negative sign indicates slowing down).

Key Terms & Definitions

• Velocity — Rate of change of displacement with direction, measured in m/s.
• Speed — Rate of change of distance, no direction, measured in m/s.
• Acceleration — Rate of change of velocity, measured in m/s².
• Instantaneous — Value at a specific moment as time approaches zero.
• Average — Value over a finite time interval.

Action Items / Next Steps

• Practice converting between units (km/h, m/s, mph).
• Memorize and practice using v_f = v_i + at and a = (v_f – v_i) / t.
• Prepare tables of time and velocity to understand linear acceleration.