Dr Pusey

Learning OutcomesDefine the following

Speed

Velocity

Acceleration

Perform calculations regarding the average speed and velocity of a moving object.

Determine the change in velocity for a moving object

Calculate the acceleration of a moving object

Speed and velocity Are speed and velocity the same thing? If they are not,

how are they different?

Speed and velocity Are speed and velocity the same thing? If they are not,

how are they different?

Noooo! Velocity is a vector quantity, speed is a scalar quantity.

Revisit 2.1 if you are not sure what this means…

Instantaneous Speed/Velocity Refers to the speed/velocity at a particular moment or

instant in time.

e.g. Speedometer on a car or GPS speed/velocity

This number is only good for an instant of time, and not for a time period

Averaged Speed/Velocity Refers to the speed/velocity averaged over a period of time

(also known as a time interval)

e.g. “Based on how long it took me to get here, I was travelling at 90km/h!”

In reality, you probably spent some time travelling at 100km/h, and some time travelling at 80km/h

Average Speed and Velocity Calcs Average Speed =

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑇𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑

𝑇𝑖𝑚𝑒 𝑇𝑎𝑘𝑒𝑛=

𝑠

∆𝑡

Average Velocity = ?

Average Speed and Velocity Calcs Average Speed =

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑇𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑

𝑇𝑖𝑚𝑒 𝑇𝑎𝑘𝑒𝑛=

𝑠

∆𝑡

Average Velocity = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑇𝑖𝑚𝑒 𝑇𝑎𝑘𝑒𝑛=

𝒔

∆𝑡

Try the Worked Example (HP 2.2A) Damian jogs 100m north in a time of 20s. He then

turns and walks 50m south in 25s before stopping.

A) Calculate his average speed when jogging

B) What is his average velocity when jogging

C) What is the average speed for the whole exercise?

D) What is the average velocity for the whole exercise?

E) What is the average velocity in km/h?

Try the Worked Example (HP 2.2A) A) Calculate his average speed when jogging

Average Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑇𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑

𝑇𝑖𝑚𝑒 𝑇𝑎𝑘𝑒𝑛=

𝑠

∆𝑡=

100𝑚

20𝑠= 5.0𝑚/𝑠

B) What is his average velocity when jogging

Average Velocity = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑇𝑖𝑚𝑒 𝑇𝑎𝑘𝑒𝑛=

𝒔

∆𝑡=

𝟏𝟎𝟎𝒎𝑵𝒐𝒓𝒕𝒉

20 𝑠

=5.0 m/s North

Try the Worked Example (HP 2.2A) C) What is the average speed for the whole exercise?

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑇𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑

𝑇𝑖𝑚𝑒 𝑇𝑎𝑘𝑒𝑛=

100𝑚+ 50𝑚

20𝑠+25𝑠=

150𝑚

45𝑠= 𝟑. 𝟑𝒎/𝒔

D) What is the average velocity for the whole exercise?

𝒔

∆𝑡=

𝟏𝟎𝟎𝒎𝑵𝒐𝒓𝒕𝒉+𝟓𝟎𝒎 𝑺𝒐𝒖𝒕𝒉

45𝑠=

𝟓𝟎𝒎𝑵𝒐𝒓𝒕𝒉

45𝑠= 𝟏. 𝟏𝐦/𝐬 North

E) What is the average velocity in km/h? = (1.1 / 1000)*3600= 4.0km/h

Acceleration So, Velocity is CHANGE IN POSITION WITH TIME

∆𝒔

∆𝑡

Acceleration is CHANGE IN VELOCITY WITH TIME

What do you think the equation is?

Acceleration So, Velocity is CHANGE IN POSITION WITH TIME

𝑣𝑎𝑣 =∆𝒔

∆𝑡

Acceleration is CHANGE IN VELOCITY WITH TIME

𝐚𝐚𝐯 =∆𝒗

∆𝑡 But how do you find the change in velocity?

∆𝒗 = 𝒗 − 𝒖

v = final velocity (at the end), u = initial velocity (at the start)

Change in Velocity∆𝒗 = 𝒗 − 𝒖

If you subtract a vector, you can add the opposite vector instead!

Also, if you have a negative number, this means opposite direction

It is often helpful to designate a ‘positive’ direction

For example, if I was sprinting 10m/s North and then slowed to 7m/s North, what is my change in velocity?

Obviously, it’s 3m/s, but is it north, or south? How do you show this?

Change in Velocity∆𝒗 = 𝒗 − 𝒖

u = 10m/s North

v = 7m/s North

I’m going to say “let North be Positive” – This means anything positive means it is acting north. So:

u = +10m/s

v = +7m/s

Change in Velocityu = +10m/s

v = +7m/s

∆𝒗 = 𝒗 − 𝒖 = 7m/s - 10m/s = -3m/s

The answer is negative, so it can be written as

3m/s South

Therefore, the change in velocity was 3m/s South.

Acceleration“Therefore, the change in velocity was 3m/s South.”

Why does this matter?

Let’s revisit the acceleration equation:

𝐚𝐚𝐯 =∆𝒗

∆𝑡

If this change in velocity occurred over a 2 second time interval, what was the acceleration?

Acceleration𝐚𝐚𝐯 =

∆𝒗

∆𝑡=

3𝑚𝑠_1𝑆𝑜𝑢𝑡ℎ

2= 1.5 m/s2 South or

So, the acceleration was acting in the opposite direction to motion.

OR:

𝐚𝐚𝐯 =∆𝒗

∆𝑡=

−3𝑚𝑠_1

2= -1.5 m/s2

Therefore, the object was decelerating in the Northerly direction.

Do this one in your head:If I let go of a marble from the top of a hotel building (of course I would never do this…)

What is the marble’s acceleration after 2 seconds?

What is the marble’s velocity after 2 seconds?

ASSUME NO AIR RESISTANCE

HP Worked Example 2.2CTry this yourself before completing the chapter questions (no peeking!)

A golf ball is dropped onto a concrete floor and strikes the floor at 5.0 m/s. It then rebounds at 5.0m/s.

What is the change in speed?

What is the change in velocity?

Handy Tips You will (not ‘might’) make mistakes occasionally when

forgetting to use the correct sign (negative/positive) and/or forgetting to include direction.

This can be minimised with practise and proper setting out!

Always use the “reasonableness test’ to assert whether or not your answers are sensible.

“My answer says the ball is accelerating in the opposite direction. So it must be slowing down… Is it?”

How did you go?Define the following

Speed

Velocity

Acceleration

Perform calculations regarding the average speed and velocity of a moving object.

Determine the change in velocity for a moving object

Calculate the acceleration of a moving object