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m1 proof for kinematic formulae

can anyone post up the proof for the formulae as proved in the heninemann m1 book. i am trying to prove them but i can't do it nor do i have the book. thanks
i think there were 3 or 4 formulae e.g. v= u + at; etc.... thanks :tsr2:
Reply 1
Avatar for yazan_l
yazan_l
5
why do u need their proofs?
Reply 2
Avatar for RoosterDude
RoosterDude
Do you need proofs as to why they work or will this do:

d/dt(s) = d/dt(ut + ½at²)
v = u + at

then:
d/dt(v) = d/dt(u + at)
a = a

That's proof enough!
Reply 3
Avatar for arslan
arslan
OP
2
yazan_l
why do u need their proofs?


sorry, very simple proof, only how to get to the formulae; not proving that they work.

for example, i think you start with a = (v-u)/t and use other formulae to set up simultaneous eqn.s and then the other formulae can be derived.

never mind, it's just something thats on my mind as i can't remeber. it's in the m1 book anyway i'll take a look when i get one, but it'll b helpful if someone could copy it out.
Reply 4
Avatar for RoosterDude
RoosterDude
Oh ok, start with v = u + at which I'll call 1 and s = 0.5(u + v)t which I'll call 2

sub for v into 2: s = 0.5(u + u +at)t => s = ut + 0.5at²

If v = u + at it follows that t = (v - u)/a
sub this into 2: s = 0.5 (u + v)(v - u) / a => s = v² - u² / 2a => v² = u² + 2as

And finally if v = u + at it follows that u = v - at
sub this into 2: s = 0.5(2v-at)t => s = vt - 0.5at²

And there you have it, a full set of SUVAT equations (valid only for constant acceleration). Also note that each one of the equations omits a different variable, hence me eliminating them above! :smile:
Yeah... and to come up with v = u + at you can just draw a velocity/time graph, noting that acceleration is the gradient of the line. Same with s = ut + 1/2 at^2, except that distance is area under the graph.

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