2 - kinematics

distance

a scalar quantity with magnitude only
it is a measure of how far an object travels

displacement

a measure of how far something is from its starting position, along with its direction
in other words, it is the change in position
it is a vector quantity with both magnitude and direction

example of distance

• Consider some athletes running a 300 m race on a 400 m track

• The distance travelled by the athletes is 300 m

example of displacement (using same situation as distance)

• Consider the same 300 m race again

  • The athletes have still run a total distance of 300 m (this is indicated by the arrow in red)

  • However, their displacement at the end of the race is 100 m to the right (this is indicated by the arrow in green)

  • If they had run the full 400 m, their final displacement would be zero

why is distance a scalar quantity

because it describes how far an object has travelled overall, but not the direction it has travelled in

why is displacement a vector quantity

because it describes how far an object is from where it started and in what direction

speed

the distance an object travels every second
it’s a scal

equation for a average speed

total distance/time taken

SI units for speed

meters per second (ms-1) but speed can often be measured in alternative units e.g. km h⁻¹ or mph, when it is more appropriate for the situation

velocity

the rate of change of displacement
it is a vector quantity with both magnitude and direction - it is the speed in a given direction

equation for average velocity

total displacement (in m)/total time taken (s)

• If the initial velocity u and final velocity v are known, the average velocity can also be calculated using:

u + v / 2

examiner tip - Velocity is speed in a given direction, but average velocity is not average speed in a given direction. This is because speed uses distance, and velocity uses displacement, and the magnitudes of these values can be very different for the same motion. 

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acceleration

the rate of change of velocity

it is a vectory quantity

unit of acceleration

ms-2 )

equation for average acceleration

change in velocity/time taken

change in velocity equation

final velocity - initial velocity