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Mechanics Chapter 2 :: �Constant Acceleration

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Chapter Overview

1:: Displacement time graphs.

 

2:: Speed/Velocity time graphs.

 

3:: Acceleration time graphs.

 

4:: Problem solving suvat.

 

5:: Vertical Motion under gravity.

 

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RECAP :: Displacement-Time Graphs

Describe the motion of each object:

 

 

 

 

 

 

Object is stationary.

Object is moving with constant velocity.

Object is accelerating.

Velocity is the rate of change of displacement

(i.e. gradient of displacement-time graph)

 

Displacement from starting point

Time taken

 

Total distance travelled

Time taken

The distinction is important. If you went out then some time later travelled back home, your average velocity is 0 because your eventual displacement is 0!

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Example

[Textbook] A cyclist rides in a straight line for 20 minutes. She waits for half an hour, then returns in a straight line to her starting point in 15 minutes. This is a displacement-time graph for her journey.

  1. Work out the average velocity for each stage of the journey in km h-1.
  2. Write down the average velocity for the whole journey.
  3. Work out average speed for the whole journey.

 

 

5

20

50

65

 

 

 

 

 

a

b

c

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Exercise 2A

Pearson Mechanics 1

Pages 12-13

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RECAP :: Velocity-Time Graphs

Describe the motion of each object:

 

 

 

 

 

 

Object is stationary.

Object is moving with constant velocity (as change in velocity is 0).

Object has constant acceleration (as velocity is increasing at constant rate).

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Acceleration is the rate of change of velocity

(i.e. gradient of velocity-time graph)

The area under a velocity-time graph gives the distance travelled.

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Fro Note: We’ll see later in Chapter 11 that when we differentiate displacement we get velocity, and therefore integrating velocity gives displacement. But we know that integrating finds the area under the graph.

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Examples

[Textbook] The figure shows a velocity-time graph illustrating the motion of a cyclist moving along a straight road for a period of 12 seconds. For the first 8 seconds, she moves at a constant speed of 6 m s-1. She then decelerates at a constant rate, stopping after a further 4 seconds.

  1. Find the displacement from the starting point of the cyclist after this 12 second period.
  2. Work out the rate at which the cyclist decelerates.

 

 

6

8

12

 

a

b

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Algebraic Example

 

 

 

8

 

 

 

 

 

 

 

Fro Tip: Sometimes it’s easier to indicate the period of time that has passed (using arrows) rather than the time at the end of the interval.

 

a

b

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Test Your Understanding

Edexcel M1 May 2013

You won’t likely have the knowledge for (d) yet…

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Exercise 2B

Pearson Mechanics 1

Pages 15-16

Edexcel M1 May 2012 Q4

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“suvat” equations (Part 1)

When there is constant acceleration, there are a variety of formulae which relate the following 5 quantities:

 

Velocity

Time

 

 

 

 

Each “suvat” equation we will see involves 4 of the 5 quantities. Typically in a problem we’ll know 3 of the quantities and we wish to find an unknown 4th quantitiy. We therefore select the appropriate equation.

You are expected to be able to prove each “suvat” question using the above graph.

 

 

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Examples

[Textbook] A cyclist is travelling along a straight road. She accelerates at a constant rate from a velocity of 4 ms-1 to a velocity of 7.5 ms-1 in 40 seconds. Find:

  1. the distance she travels in these 40 seconds
  2. her acceleration in these 40 seconds.

 

a

b

Always write each letter of suvat, putting a “?” for any quantities you need to find.xx

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Examples

 

 

As stated before, think about what period of time we’re considering.

 

a

c

d

b

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Test Your Understanding

[Textbook] A car moves from traffic lights along a straight road with constant acceleration. The car starts from rest at the traffic lights and 30 second later the car passes a speed-trap where it is registered as travelling at 45 km h-1. Find:

  1. the acceleration of the car
  2. the distance between the traffic lights and the speed-trap.

Tip: Ensure everything is in SI units first.

 

a

b

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Exercise 3C

Pearson Mechanics 1

Pages 18-19

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“suvat” equations (Part 2)

 

 

 

 

 

 

 

 

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Examples

 

 

 

 

 

 

a

b

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Test Your Understanding

Edexcel M1 May 2013 Q4

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Exercise 2D

Pearson Mechanics 1

Pages 22-23

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Vertical Motion Under Gravity

 

 

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Example

[Textbook] A book falls off the top shelf of a bookcase. The shelf is 1.4 m above a wooden floor. Find:

  1. the time the book takes to reach the floor,
  2. the speed with which the book strikes the floor.

 

 

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a

b

 

As per previous slide, quote only to 2 significant figures. You may be penalised if you quote more!

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Further Example

 

 

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A further common type of question…

A ball is projected vertically upwards from ground level at a speed of 20 ms-1.

Determine the amount of time the ball is at least 10m above ground level.

10m

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Froculator Tip: Be sure to use the quadratic solver on your calculator (within ‘Equation’ mode on the ClassWiz).

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Test Your Understanding

Edexcel M1 May 2013(R) Q4

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Exercise 2E/2F

Pearson Mechanics 1

Pages 27-28 & 33-34