Displacement, Instantaneous and average speed, velocity,

acceleration and position-time graphs. (Catchy title, huh?)

Year 12

Unit 1

Module 1

Lesson 4

• A man walks round a circle of radius 20m, arriving back where he started after 2 minutes

• What was the average velocity of the man, in ms-1?

20m

• If you said about 1.05ms-1… you’d be wrong

Last week…

• F cos θ (Resolving Vectors)

• F sin θ

• Vector addition

Back to the man walking in circles

• The answer is…

• 0 ms-1

• But why?

• We use displacement to calculate velocity, displacement is a vector, and the man’s start and finish location are the same – therefore, displacement is 0, and so is average velocity.

•

• Or in words:

velocity = displacement / time

• What about speed?

Speed = distance / time

Food for thought…

• How can you go 200 mph in a 50 mph average speed check zone?

• We will come back to this later on…

Experiment (Sort of)

• Bring Pen, Paper, Calculator, and your coat if you want to…

• So… we have 2 types of velocity / speed to worry about. Instantaneous and average.

Instantaneous Velocity Average Velocity

Velocity of an object at any given instant of time

Velocity over a given time interval

Describes velocity only at that exact moment of time

Describes the mean velocity over the time period. It does not refer to top velocity, or even mean that the object was travelling at that velocity very long

v=s/t Δv = Δs/Δt

• In our rocket experiment…

• Would the average speed or the average velocity be higher or the same?

• Higher, but why?

• Displacement is a vector, so is only concerned about the distance it travelled, where as distance counts the path taken.

Distance vs Displacement

The difference between displacement and distance is shown opposite. An object moves from A to B along the line AXYB. The distance travelled from A to B is shown by the line AXYB while the displacement is shown by the vector AB.

B

A

Y

X

What is velocity?

• So what does that make acceleration?

Velocity is rate of change of position of an object, specified by it’s magnitude and direction.

What is acceleration?

Acceleration is the rate of change of the velocity of a body

• So what will be our formula for acceleration? What units will it have?

𝑎=𝑣−𝑢𝑡

• Units are ms-2

• v = final velocity; u = initial velocity; t = time; a = acceleration

• If you are going from stationary, u = 0

• A negative acceleration is slowing down

• Note for the future: Acceleration is closely linked with force, in fact it is proportional to force.

𝑎=𝑣−𝑢𝑡

Review Questions1) A car brakes from 25m/s to 10m/s in 5sec what is its acceleration? At its final speed how long will it take to cover 2.5km?

2) A dragster has an acceleration of 4.905 ms-2how long will it take it to go from rest to 50m/s?

3) A rocket accelerates from stand still to escape velocity, 11,200 ms-1. It takes 10 minutes to reach this speed. What is the acceleration the rocket experiences?

4) A car goes from 0ms-1 to it’s top speed in 6.5s, with an acceleration of 25ms-2.

Position-Time graphs

Uniform velocity - constant

ReminderVelocity = displacement / timev = s/tThereforeDisplacement = velocity x times= v t

Template copyright www.brainybetty.com 2005 1815/09/06

•

•Draw a displacement –time graph for bob’s journey. Distance should be along the y-axis, and time on the x-axis

•Bob is out for a walk. He starts travelling at 0.5m/s for 20 secs• He then jogs on for 10 secs at a speed of 5m/s• He then stops for 10 seconds to remember what he forgot but can't.• He suddenly remembers what it was and walks back at for 20 secs at 3m/s

Each type of motion on a displacement-time graph

• Slide coming soon, to a whiteboard near you!• (Probably just want to write them down for now)

15/09/06

• How can we work out velocity from a displacement-time graph?

• Velocity is rate of change of position.

• We need to find out how rapidly the position is changing

• Our graph lets us do this easily – it’s simply the gradient!!!

• What about distance-time graphs?

• Can we have a negative value on a distance-time graph?

• No – distance is just the path taken, it had no direction, hence negative distance doesn’t really mean anything

• What would the gradient of a distance-time graph be?

• Speed, speed = distance/time

• Write 3 questions on a piece of paper. Anything from this lesson…

Homework (due 27/09/13)

• Draw a displacement-time and a distance-time graph of your journey to school (or any hypothetical journey, so long as you can explain the motion) and write a list of how your motion changed over the course of the journey.

• E.g. 0 – 1 mins, I accelerated to walking pace of 1.6ms-1 over 5 metres

• 1-10 mins, I walked at a steady pace of 1.6ms-1 for 600 metres

• 10-11 mins, I accelerated to running speed of 7ms-1 when I realised I forgot my homework for Mr. Mason, 605 metres back the direction I came

• Etc. (…and obviously draw the appropriate graphs)