2.1.3 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 s^–2)
  • Δv = change in velocity in metres per second (m s^–1)
  • 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

Equations linking displacement, velocity, and acceleration

Speeding Up and 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)

Part (a)

Step 1: List the known quantities

• • Initial velocity = 50 m s^–1
  • Final velocity = 42 m s^–1

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^–1

Part (b)

Step 1: List the known quantities

• • Change in velocity, Δv = −8 m s^–1
  • 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^–1

Step 4: Interpret the value for deceleration

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