Chapter 3: Motion

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Equation for speed with the units

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Equation for speed with the units

speed (ms-1) = distance (m) / time (s)

<p>speed <span style="color: purple">(ms<sup>-1</sup>)</span> = distance<span style="color: purple"> (m)</span> / time <span style="color: purple">(s)</span></p>
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Definition of speed

Rate of change of distance

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The x-axis and y-axis on a distance-time graph

x-axis: Time (s)

y-axis: Distance (m)

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How are:

  • Stationary objects

  • Objects moving at a constant speed

  • Objects with varying speed

portrayed on a distance-time graph?

Stationary objects: horizontal line

Constant speed: sloping straight line

Varying speed: curved line

<p><span style="color: blue">Stationary objects</span>: horizontal line</p><p><span style="color: blue">Constant speed</span>: sloping straight line</p><p><span style="color: blue">Varying speed</span>: curved line </p>
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Instantaneous speed

The speed at any given point in time

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Finding the instantaneous speed on a distance-time graph

  • Draw a tangent

  • Calculate the gradient of the tangent = speed

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How is the acceleration found on a speed-time graph?

The gradient

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How is the speed found on a distance-time graph?

The gradient

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How is the distance found on a speed-time graph?

Area under the graph

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How is the velocity found on a displacement-time graph?

The gradient

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Equation for velocity with units

velocity (ms-2) = change in displacement (m) / time (s)

<p>velocity <span style="color: purple">(ms<sup>-2</sup>)</span> =  change in displacement <span style="color: purple">(m)</span> / time <span style="color: purple">(s)</span></p>
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Definition of velocity

Rate of change of displacement

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Equation for acceleration with units

acceleration (ms-2) = change in velocity (ms-1) / change in time (s)

<p>acceleration <span style="color: purple">(</span><span style="color: purple">ms<sup>-2</sup>)</span><span> = </span>change in velocity <span style="color: purple">(m</span><span style="color: purple">s<sup>-1</sup></span><span style="color: purple">)</span> /  change in time <span style="color: purple">(s)</span></p>
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Define acceleration

Rate of change of velocity. Is a vector quantity.

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How are:

  • Stationary objects

  • Objects moving at a constant velocity

  • Objects with varying velocity

  • Objects with increasing / decreasing velocity

portrayed on a velocity-time graph?

Stationary objects: horizontal line along the x-axis

Constant velocity: horizontal line not on the x-axis

Varying velocity: curved line

Increasing velocity: straight line +ve gradient

Decreasing velocity: straight line -ve gradient

<p><span style="color: blue">Stationary objects</span>: horizontal line along the x-axis</p><p><span style="color: blue">Constant velocity</span>: horizontal line not on the x-axis</p><p><span style="color: blue">Varying velocity</span>: curved line</p><p><span style="color: blue">Increasing velocity</span>: straight line +ve gradient </p><p><span style="color: blue">Decreasing velocity</span>: straight line -ve gradient </p>
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What is the area under a velocity-time graph?

Distance / displacement

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The distance of a non-linear velocity-time graph

Count the squares under the graph - only if the majority is under the curve

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Draw a these graphs for a bouncing ball:

  • displacement-time graph

  • velocity-time graph

  • acceleration-time graph

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What are SUVAT equations used for?

constant acceleration

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What does

S U V A T

stand for?

S displacement
U initial velocity
V final velocity
A acceleration
T time taken for the change in velocity

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If an object starts from rest, what is the initial velocity / time taken for the change in velocity?

u = 0

t = 0

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If an object’s initial velocity isn’t mentioned, what is the initial velocity?

u = 0

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What can be infered if an object is falling due to gravity in regards with SUVAT equations?

a = g = 9.81 ms-2

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Components of the stopping distance

  • Thinking distance

  • Braking distance

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Thinking distance

Distance travelled by the vehicle from when the driver sees a problem and applies the brake

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Formula of the thinking distance

Thinking distance = initial speed x reaction time

Proportional to the initial speed (u)

Time taken for the driver to respond to the problem

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Factors affecting the thinking distance

  • initial speed

  • tiredness

  • age

  • distraction

  • medication

  • eyesight

  • under the influence

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Braking distance

The distance travelled by the vehicle after the driver has applied to the brake

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Equation for braking distance

Time period when brakes are applied x average speed

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Equation for work done by the brakes

Work done = braking force x braking distance x ½ mv2

Proportional to the square of the initial speed (u2)

All of the vehicles kinetic energy (½ mv2) must be dissipated by the brakes in order to stop

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Factors affecting braking distance

  • mass of the vehicle

  • weather conditions

  • initial speed

  • car condition (e.g. tyres, brakes etc.)

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The interaction with the thinking and braking distance and speed

Thinking distance increasing proportionally with speed:

  • if the speed doubles, the thinking distance doubles

the braking distance increases at an even faster rate

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Acceleration due to gravity

Objects with mass (mass-energy) exerts a force upon objects that have a force, known as gravitational force. The earth is very big so it forces objects to accelerate towards the centre of the Earth.

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Free-fall

When an object is falling with no other forces acting on (ONLY IT’S OWN WEIGHT)

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What is free fall denoted by?

g - 9.81 ms-2

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Variation in the value of g

Varies slightly around the Earth due to longitude, latitude and the local geology as it's not a perfect sphere

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Projectile

An object thrown at an angle to the horizontal

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Analysing projectile motion

  • the horizontal and vertical components of the object’s motion are analysed independantly, but the time is interchangeable

  • assume there is no air resistance

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Time of flight of a projectile

How long the projectile is in the air

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Maximum height of a projectile

The height at which the projectile is momentarily at rest

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Range of a projectile

The horizontal distance travelled by the projectile

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The horizontal acceleration of a projectile

Zero

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The horizontal velocity of a projectile

Constant

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The vertical acceleration of a projectile

9.81ms-2 downwards

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When is a projectile at the maximum height?

When the vertical v = 0

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When does a projectile reach the ground?

When the vertical s = 0

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What is the time taken to reach the maximum height (for a projectile?)

Half the total time in the air

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The components of the horizontal vector (Fx)

Fx = F (cos (θ) )

in the x direction

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The components of the vertical vector (Fy)

Fy = F (sin (θ) )

in the y direction

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The angle made by the vector to the horizontal

tan θ = Fy / Fx

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