5.4.13 Calculating Uniform Acceleration

• What is uniform acceleration in physics?

  Uniform acceleration means that the acceleration of an object remains constant over time.
• What does uniform acceleration imply about the rate of change of velocity?

  It implies that the rate of change of velocity is steady over time.
• What are the key equations for calculating uniform acceleration?

  1. Final Velocity Equation: \( v = u + at \)

  2. Displacement Equation: \( s = ut + \frac{1}{2}at^2 \)

  3. Final Velocity Squared Equation: \( v^2 = u^2 + 2as \)

  4. Displacement and Average Velocity: \( s = \frac{(u + v)}{2} \times t \)
• What does the variable \( v \) represent in the final velocity equation?

  \( v \) represents the final velocity in meters per second (m/s).
• What does the variable \( u \) represent in the equations for uniform acceleration?

  \( u \) represents the initial velocity in meters per second (m/s).
• What does the variable \( a \) represent in the equations for uniform acceleration?


  \( a \) represents acceleration in meters per second squared (m/s²).
• What does the variable \( t \) represent in the equations for uniform acceleration?

  \( t \) represents time in seconds (s).
• If an object starts from rest and reaches a velocity of 20 m/s in 5 seconds, how do you calculate its acceleration?


  Use the equation \( a = \frac{v - u}{t} \).
• What is the acceleration of an object that starts from rest and reaches a velocity of 20 m/s in 5 seconds?

  The acceleration is \( 4 \text{ m/s}^2 \).
• How do you calculate the displacement of an object with an initial velocity of 10 m/s accelerating at 2 m/s² for 6 seconds?

  Use the equation \( s = ut + \frac{1}{2}at^2 \).
• What is the displacement of an object with an initial velocity of 10 m/s, accelerating at 2 m/s² for 6 seconds?

  The displacement is 96 meters.
• How do you calculate the final velocity of an object accelerating uniformly at \( 3 \text{ m/s}^2 \) from an initial velocity of \( 5 \text{ m/s} \) over \( 8 \text{ seconds} \)?


  Use the equation \( v = u + at \).
• What is the final velocity of an object that accelerates uniformly at \( 3 \text{ m/s}^2 \) from an initial velocity of \( 5 \text{ m/s} \) over \( 8 \text{ seconds} \)?

  The final velocity is \( 29 \text{ m/s} \).
• How do you calculate the acceleration of an object that accelerates from \( 2 \text{ m/s} \) to \( 12 \text{ m/s} \) over a distance of 40 meters?

  Use the equation \( a = \frac{v^2 - u^2}{2s} \).
• What is the acceleration of an object that accelerates from \( 2 \text{ m/s} \) to \( 12 \text{ m/s} \) over a distance of 40 meters?

  The acceleration is \( 1.75 \text{ m/s}^2 \).
• What is the summary of uniform acceleration and its applications?


  • Uniform acceleration is the constant rate of change of velocity.
  • Key equations include:
  • \( v = u + at \)
  • \( s = ut + \frac{1}{2}at^2 \)
  • \( v^2 = u^2 + 2as \)
  • \( s = \frac{(u + v)}{2} \times t \)
  • Applications include solving problems related to motion with constant acceleration, such as free-falling objects and accelerating vehicles.
• What does uniform acceleration mean in GCSE Physics?

  It means the acceleration remains constant throughout the motion.
• What are the key equations for uniform acceleration?

  1. Final Velocity Equation: \( v = u + at \)

  2. Displacement Equation: \( s = ut + \frac{1}{2}at^2 \)

  3. Final Velocity Squared Equation: \( v^2 = u^2 + 2as \)

  4. Average Velocity for Displacement: \( s = \frac{(u + v)}{2} \times t \)
• What does the variable \( v \) represent in the final velocity equation?


  Final velocity (m/s)
• What does the variable \( u \) represent in the final velocity equation?

  Initial velocity (m/s)
• What does the variable \( a \) represent in the final velocity equation?

  Acceleration (m/s²)
• What does the variable \( t \) represent in the final velocity equation?

  Time (s)
• What does the variable \( s \) represent in the displacement equation?

  Displacement (m)
• How do you rearrange the final velocity equation to solve for acceleration \( a \)?

  By using the formula \( a = \frac{v - u}{t} \)
• If a car accelerates from 10 m/s to 30 m/s in 5 seconds, what is its acceleration?

  4 m/s²
• What is the displacement of a bike that accelerates uniformly from rest at a rate of 2 m/s² for 8 seconds?

  64 meters
• How do you calculate the displacement using the equation \( s = ut + \frac{1}{2}at^2 \) when \( u = 0 \text{ m/s} \), \( a = 2 \text{ m/s}^2 \), and \( t = 8 \text{ s} \)?

  Substituting gives \( s = 64 \text{ meters} \)
• What is the final velocity of an object that starts with a velocity of 5 m/s and accelerates uniformly at 3 m/s² over a distance of 50 meters?

  Approximately 18.03 m/s
• How do you find the final velocity using the equation \( v^2 = u^2 + 2as \) when \( u = 5 \text{ m/s} \), \( a = 3 \text{ m/s}^2 \), and \( s = 50 \text{ m} \)?


  By calculating \( v = \sqrt{325} \approx 18.03 \text{ m/s} \)
• What is the displacement of a car that accelerates from 20 m/s to 40 m/s over 10 seconds?

  300 meters
• How do you calculate displacement using the average velocity equation \( s = \frac{(u + v)}{2} \times t \) when \( u = 20 \text{ m/s} \), \( v = 40 \text{ m/s} \), and \( t = 10 \text{ s} \)?

  By substituting to find \( s = 300 \text{ meters} \)
• What are the applications of the key equations of motion for uniformly accelerated motion?

  • Solving problems involving objects with constant acceleration
  • Examples include free-falling objects and vehicles in motion
• What is the summary of uniform acceleration and its key equations?


  • Uniform acceleration: Acceleration remains constant
  • Key equations:
  • \( v = u + at \)
  • \( s = ut + \frac{1}{2}at^2 \)
  • \( v^2 = u^2 + 2as \)
  • \( s = \frac{(u + v)}{2} \times t \)