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Unit 1.1 - Kinematics
Scalars and Vectors
A quantity in Physics is something that can be measured. Any quantity is either a scalar or a vector.

A scalar quantity is fully described by its Magnitude (size) including its unit of measurement.
A vector quantity is fully described by its Magnitude…

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A cyclist is going on a journey round a country road.

If the red line represents a country road, then the distance the bike has to travel is




5km.
If the green line represents the displacement, then the displacement of the whole journey is 2km.




Speed and Velocity.

The speed…

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The velocity of an object is calculated by:

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Both of these are represented by:




Adding scalars and vectors



Adding scalars is easy ­ the magnitudes add up.

Adding vectors is not so easy ­ the direction means we cannot just add the magnitudes.

We add vectors using diagrams. Vectors are drawn as arrows.

The length of the arrow…

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This routine is sometimes known as adding vectors "tip to tail".



Vector tip Vector tail




Acceleration

The acceleration of an objects it its change of velocity with time.




The equation for acceleration is:








Where:

a = acceleration (ms-2)

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v = final speed (ms-1)

u = initial speed (ms-1)

t ­ time taken (s)



The acceleration equation re-arranged for final speed is...




The acceleration equation re-arranged for initial speed is...




The acceleration equation re-arranged for time is...




Instantaneous & Average Speed



Average speed is a measure of the distance…

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Let's say you are going on a car journey. You travelled a distance of 5 miles and the trip lasted 0.2
hours (12 minutes). The average speed of your car can be found by using the speed, distance time
equation.




Where:

V= SPEED (MS-1)

S =distance travelled (m)

T= time…

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Your car may have been moving at speed of 25 miles per hour (this is an average speed)

BUT, during your trip, there may have been times that you were stopped and other times that your
speedometer was reading 50 miles per hour (this is an instantaneous speed).




Velocity time…

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