Kinematics:

 

Kinematics is the physics of motion!

Similarities and differences between distance and displacement:

 

 

Distance

Displacement

Units:

Meters

Meters

Quantity:

Scalar

Vector

Representation:

By number and unit

e.g. 5m 10km

Represented by a vector arrow

 

 

 

 

 

 

 

 

 Distance = 50 + 60 + 35 + 40

          = 185 m

Dispalcement = (√502+602) + (√352+402)

        = 131. (3sf)

 tan-1 100/85

= 49.6°

 Vector is 131m at angle of 49.6° due north

 Equations of motion for an object traveling at constant acceleration:

 u = initial velocity

v = final velocity

t  = time taken

s = displacement

a = acceleration

 Acceleration = Δ Velocity / Δ Time

 at = v - u 

v = u + at – EQUATION 1

 Average velocity = distance moved / time taken

 (u + v) / 2 = s / t

therefore: s = (u + v) / 2 x t – EQUATION 2

 t = 2s / (u + v)

v = u + a (2s / (u + v))

v – u = a (2s / (u+v))

(v-u)(v+u) = 2as

v2 – u2 = 2as

v2 = u2 + 2as -  EQUATION 3

 From 2)

s = (u+v) / 2  x t

but we can sub in equation 1 for the v, so we get:

 s = (u + u + at)t  / 2

s = (2u + at)t / 2

s = 2ut + at2 / 2

s = ut + ½at2 – EQUATION 4