Calculating Uniform Acceleration (OCR Gateway GCSE Physics: Combined Science)

• 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)

• 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

Part (a)

Step 1: List the known quantities

• • Initial velocity = 50 m/s
  • Final velocity = 42 m/s

Step 2: Write the relevant equation

change in velocity = final velocity − initial velocity

Step 3: Substitute values for final and initial velocity

change in velocity = 42 − 50 = −8 m/s

Part (b)

Step 1: List the known quantities

• • Change in velocity, Δv = − 8 m/s
  • Time taken, t = 30 s

Step 2: Write the relevant equation

Step 3: Substitute the values for change in velocity and time

a = −8 ÷ 30 = −0.27 m/s

Step 4: Interpret the value for deceleration

• • The answer is negative, which indicates the train is slowing down

Step 1: Identify and write down the equation to use

• • The question says that the car 'accelerates steadily' - so the equation for uniform acceleration can be used:

v² − u² = 2 × a × x

Step 2: List the known quantities

• • Initial speed, u = 0 m/s (the car starts from rest)
  • Final speed, v = 16 m/s
  • Acceleration, a = 2.5 m/s²
  • Distance, x = ? (this needs to be calculated)

Step 3: Substitute known quantities into the equation and simplify where possible

16² − 0² = (2 × 2.5 × x)

• • This can be simplified to:

256 = 5 × x

Step 4: Rearrange the equation to work out the distance travelled

x = 256 ÷ 5

x = 51.2 m

Kinetic Energy

• The kinetic energy (E_k 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:

E_k = ½ × m × v²

• Where:
  • E_k = 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

Step 1: List the known quantities

• • Mass of the vehicle, m = 1200 kg
  • Speed of the vehicle, v = 27 m/s

Step 2: Write down the equation for kinetic energy

E_k = ½ mv²

Step 3: Calculate the kinetic energy

E_k = ½ × 1200 × (27)² = 437 400 J

Step 4: Round the final answer to 2 significant figures

E_k = 440 000 J