Calculating Uniform Acceleration

• Calculating Uniform Acceleration:

  • Acceleration is defined as the rate of change of velocity
  • In other words, it describes how much an object's velocity changes every second
• • The equation below is used to calculate the average acceleration of an object:

  
• • Where:
  • a = acceleration in metres per second squared (m/s2)
  • Δv = change in velocity in metres per second (m/s)
  • t = time taken in seconds (s)
• • The change in velocity is found by the difference between the initial and final velocity, as written below:

  change in velocity = final velocity − initial velocity

  Δv = v − u
• • Where:
  • v = final velocity in metres per second (m/s)
  • u = initial velocity in metres per second (m/s)
• • The equation for acceleration can be rearranged with the help of a formula triangle as shown:

  
• Speeding Up & Slowing Down:

  • An object that speeds up is accelerating
  • An object that slows down is decelerating
  • The acceleration of an object can be positive or negative, depending on whether the object is speeding up or slowing down
  • If an object is speeding up, its acceleration is positive
  • If an object is slowing down, its acceleration is negative (sometimes called deceleration)
• A rocket speeding up (accelerating) and a car slowing down (decelerating):

  
• Uniform Acceleration:

  • The following equation of motion applies to objects moving with uniform (constant) acceleration:

  (final speed)2 − (initial speed)2 = 2 × acceleration × distance travelled
• • Where:
  • x = distance travelled in metres (m)
  • u = initial speed in metres per second (m/s)
  • v = final speed in metres per second (m/s)
  • a = acceleration in metres per second squared (m/s2)
• Uniform Acceleration:

  • This equation is used to calculate quantities such as initial or final speed, acceleration, or distance travelled in cases where the time taken is not known
• Kinetic Energy:

  • The kinetic energy (Ek or KE) of an object (also known as its kinetic store) is defined as:

  The energy an object has as a result of its mass and speed
• • This means that any object in motion has kinetic energy:

  
• • Kinetic energy can be calculated using the equation:

  Ek = ½ × m × v2
• Where:

  • Ek = kinetic energy in Joules (J)
  • m = mass of the object in kilograms (kg)
  • v = speed of the object in metres per second (m/s)
  • Therefore, an acceleration will result in a change of kinetic energy
  • This is because the speed is changing