Acceleration (Cambridge International IGCSE Science)

Acceleration

• An object can change its speed by:

  • speeding up
  • slowing down

• When an object speeds up, it is accelerating

• When an object slows down, it is decelerating

Calculating acceleration

Extended Tier Only

• Acceleration describes how the velocity of an object changes over time
• Acceleration is defined as: The rate of change of velocity
• In other words, acceleration is the change in velocity per unit time
• The acceleration of an object is often changing throughout an object's journey
• Therefore, is it often useful to know the average acceleration

$a=\frac{\Delta v}{\Delta t}$

• Where:

  • $a$ = acceleration in metres per second squared (m/s²)
  • $\Delta v$ = change in velocity in metres per second (m/s)
  • $\Delta t$ = time taken in seconds (s)

Formula triangle for acceleration, change in velocity and change in time

To use a formula triangle, simply cover up the quantity you wish calculate and the structure of the equation is revealed

• Information on how to use a formula triangle can be found in Speed & velocity

Change in velocity

• The change in velocity is the difference between the initial and final velocity:

$\Delta v=v-u$

• Where:

  • $\Delta v$ = change in velocity in metres per second (m/s)
  • $v$ = final velocity in metres per second (m/s)
  • $u$ = initial velocity in metres per second (m/s)

• If an object speeds up, its acceleration is positive

• If an object slows down, its acceleration is negative

• Acceleration is positive if it is in the same direction as the motion of the object

Acceleration of different objects

A rocket speeding up (accelerating) and a car slowing down (decelerating)

Worked Example A Japanese bullet train decelerates at a constant rate in a straight line. The velocity of the train decreases from 50 m/s to 42 m/s in 30 seconds.

(a) Calculate the change in velocity of the train.

(b) Calculate the deceleration of the train, and explain how your answer shows the train is slowing down.

Answer:

Part (a)

Step 1: List the known quantities

• Initial velocity, $u=50m/s$
• Final velocity, $v=42m/s$

Step 2: Write the equation for change in velocity

$\Delta v=v-u$

Step 3: Substitute values for final and initial velocity

$\Delta v=42-50$

$\Delta v=-8m/s$

Part (b)

Step 1: List the known quantities

• Change in velocity, $\Delta v=-8m/s$
• Time taken, $\Delta t=30s$

Step 2: Write the equation for acceleration

$a=\frac{\Delta v}{\Delta t}$

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

$a=\frac{-8}{30}$

$a=-0.27m/s^{2}$

Step 4: Interpret the value for deceleration

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

Exam Hint Remember, the units for acceleration are metres per second squared, m/s². In other words, acceleration measures how much the velocity (m/s) changes every second, so the units are metres per second per second (m/s/s).