Lecture Notes: Calculating Velocity and Acceleration

Key Objectives

• Calculate the velocity of an object with constant acceleration.
• Describe acceleration of an object falling through a fluid.

Acceleration Recap

• Acceleration Equation: Acceleration = Change in velocity / Time (no need to memorize for exams).

Calculating Velocity with Constant Acceleration

• Equation: Final velocity squared - Initial velocity squared = 2 x Acceleration x Distance.
  • This equation is provided in exams.
  • More likely to appear on higher-tier exams.

Example Problem 1

• A car accelerates from 8 m/s to 12 m/s with an acceleration of 2 m/s².
• Distance Calculation: Rearrange the equation to solve for distance.
  • Final velocity: 12 m/s
  • Initial velocity: 8 m/s
  • Acceleration: 2 m/s²
  • Distance: 20 meters

Example Problem 2

• Cyclist accelerates from 3 m/s to 5 m/s over 50 meters.
• Acceleration Calculation:
  • Rearranged equation gives an acceleration of 0.16 m/s².

Example Problem 3

• Train accelerates from 20 m/s with an acceleration of 5 m/s² over 50 meters.
• Final Velocity Calculation:
  • Calculate using rearranged equation.
  • Final Velocity: 30 m/s

Acceleration Towards Earth

• Objects initially accelerate at 9.8 m/s² due to gravity.

Skydiver Example

• Forces Involved:
  • Gravity causes initial acceleration.
  • Air resistance is an upward force.
• Terminal Velocity:
  • Occurs when air resistance equals gravitational force; object stops accelerating and moves at constant velocity.
  • Dependent on object shape and friction force.

Additional Resources

• Check the revision world book for more questions on acceleration.