Acceleration (SQA National 5 Physics): Revision Note

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 relationship used to calculate the average acceleration of an object is:

$\mathrm{acceleration}=\frac{\mathrm{change}\mathrm{in}\mathrm{velocity}}{\mathrm{time}\mathrm{taken}}$

$a=\frac{∆v}{t}$

• Where:

  • $a$ = acceleration in metres per second squared (m s^-2)

  • $∆v$ = change in velocity in metres per second (m s^-1)

  • $t$ = time taken in seconds (s)

Relationship triangle for acceleration, change in velocity and time

• A more detailed explanation of how to use relationship triangles is covered in the revision note on motion relationships

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

$\mathrm{change}\mathrm{in}\mathrm{velocity}=\mathrm{final}\mathrm{velocity}-\mathrm{initial}\mathrm{velocity}$

$∆v=v-u$

• Where:

  • $v$ = final velocity in metres per second (m s^-1)

  • $u$ = initial velocity in metres per second (m s^-1)

• Therefore, the relationship for acceleration, or the rate of change of velocity, can be written as:

$a=\frac{v-u}{t}$

Speeding up and slowing down

• An object that speeds up is accelerating

• An object that slows down is decelerating

• Acceleration is a vector quantity, therefore, it 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 (also known as deceleration)

Examples of acceleration and deceleration

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