# 5.6.10 Acceleration

### Acceleration

#### Defining 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/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

• The equation for acceleration can be rearranged with the help of a formula triangle as shown: Acceleration, change in velocity, and time formula triangle

#### 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)
• Two examples of accelerating and decelerating objects are shown in the image below 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.

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

#### Exam Tip

Remember the units for acceleration are metres per second squared, m/s2

In other words, acceleration measures how much the velocity (in m/s) changes every second, m/s/s.

### Estimating Accelerations

• The acceleration of an object is a measure of how quickly its velocity changes
• A typical family car, for example, takes around 10 seconds to go from 0 m/s to 27 m/s (roughly 60 mph)
• This is an acceleration of about 2.7 m/s2
• The table below gives some other typical accelerations:

Typical Accelerations Table #### Exam Tip

You should be able to estimate the magnitude of everyday accelerations. Memorise the examples given in the table to develop a sense of the magnitude of different accelerating objects. ### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
Close Close