The Kinemati

c Rap

Now, we’ve got a ripper topic and I’m sure you will agree

That this is mighty handy, it’s our

S, u, v, a, t

S, u, v, a, t

Mega-parsec galaxies and nanobot mechanics

All obey the rules of the “Suvat” kinematics

S is for displacement, distance with

direction

S

a is for acceleration, symbol-word connection

S a

u and v: velocity; at the start and at the

end

S , u, v, a

And t is for the time elapsed

I hope you comprehend

S , u, v,a, t

There are four equations stemming from a handy

chart

u

vVel (m/s)

Time (s) t

a1

S

And two simple rules that in form five you should have

learned by heart

u

vVel (m/s)

Time (s) t

a1

S

The chart is a generic graph of velocity and time

u

vVel (m/s)

Time (s) t

a1

S

“a” is the slope and S the area underneath the line

u

vVel (m/s)

Time (s) t

a1

S

Now if “a” is the slopeAnd on this we all agree

Then v will equal u plus the extra a times t

v = u + at

And if you square this formula, the answer

you can guess

v = u + at

Is v squared equals u squared plus the

extra 2aS

v2 = u2 + 2aS

Displacement is the area that’s underneath the line

u

vVel (m/s)

Time (s) t

a1

S

And therefore av’rage speed multiplied by elapsed time

u

vVel (m/s)

Time (s) t

1a

SS

va

v

If you put that into maths then ev’ryone

can see

Displacement, S, is equal to

a half t (u plus v)

S = 1/2.t.(u+v)

But displacement can be looked at from

another sort of angle

The area under is a block plus the top triangle

u

vVel (m/s)

Time (s) t

1a

S

If you symbolise that idea, with math’matics

unimpaired

S will equal ut plus the term half a t squared*

S = ut + 1/2at2

v = u + at v2 = u2 + 2aSS = 1/2.t.(u+v)

S = ut + 1/2at2

So there it is and there they are, the handy four

equations

v = u + at v2 = u2 + 2aSS = 1/2.t.(u+v)

S = ut + 1/2at2

And you can choose the best one for all the

situations

When acceleration’s even. Yes, you can be

quite emphatic

a is constant

v = u + at v2 = u2 + 2aSS = 1/2.t.(u+v)

S = ut + 1/2at2

You’ve got your head around these four equations

kinematic!