Acceleration

Acceleration is defined as:

The rate of change of velocity

Acceleration is a vector quantity and is measured in metres per second squared (m s^–2)
- It describes how much an object's velocity changes every second

The average acceleration of an object can be calculated using:

$a v e r a g e a c c e l e r a t i o n = \frac{c h a n g e i n v e l o c i t y}{t i m e t a k e n}$

$a = \frac{∆ v}{∆ t}$

Where:
- $a$ = average acceleration (m s^–2)
- $∆ v$ = change in velocity (m s^–1)
- $∆ t$ = total time taken (s)

The change in velocity is the difference between the initial and final velocity, as written below:

change in velocity = final velocity − initial velocity

$∆ v = (v - u)$

Equations linking displacement, velocity, and acceleration

Equation Definitions, downloadable AS & A Level Physics revision notes

Instantaneous Acceleration

The instantaneous acceleration is the acceleration of an object at any given point in time
This could be for an object with a constantly changing acceleration
- An object accelerating is shown by a curved line on a velocity-time graph

What is a negative acceleration called?

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 (deceleration)

However, acceleration can also be negative if it is accelerating in the negative direction

Acceleration Examples, downloadable IGCSE & GCSE Physics revision notes

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 an initial velocity of 50 m s^–1to a final velocity of 42 m s^–1 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:

(a)

The change in velocity is equal to

$∆ v = v - u$

Where:
- Initial velocity, u = 50 m s^–1
- Final velocity, v = 42 m s^–1

$∆ v$ = 42 − 50 = −8 m s^–1

(b)

Acceleration is equal to

$a = \frac{∆ v}{∆ t}$

Where the time taken is Δt = 30 s

$a = \frac{- 8}{30} = - 0.27 m s^{- 1}$

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

Exam Tip

Remember the units for acceleration are metres per second squared, m s^–2. In other words, acceleration measures how much the velocity (in m s^–1) changes every second, (m s^–1) s^–1

Acceleration (HL IB Physics)

Revision Note