Write the five variables u, v, a, s and t at the start of a question and fill in any values you can. Make sure all units are correct.
v = u + at s = ut + 1
v2 = u2 + 2as
__ 2 at2
u = initial velocity (m s–1), v = final velocity (m s–1), a = acceleration (m s–2), s = displacement (m), t = time (s)
In order to know which equation to use, list all of the variables given and choose the formula that has only one unknown. By substituting in the known values, you can easily solve for the missing answer.
Derivations of the equations of motion These derivations are required to be proved for Higher Level only.
Derivation of v = u + at a = v – u at = v – u
______ t
v = u + at
Derivation of s = ut + 1 Average velocity = u + v
______ 2
Average velocity = s = s
u + v
__ t
________________ ( u + (u + at) ) t 2
_________ 2
____________ 2
___________ 2
ut + 1
(2u + at)t 2ut + at2
s = ut + 1 = s = s
__ 2 at2 = s
__ 2 at2
(u + v)t = s = s
__ t
H
(formula for acceleration) (multiply both sides by t)
(add u to both sides; reverse the equation)
_ 2 at2
______ 2 (from earlier definition of average velocity)
(from earlier definition) (equate the two formulae)
(multiply both sides by t)
(substitute (u + at) for v on the left) (simplify)
(multiply out brackets) (divide terms on LHS by 2) (reverse equation)
Derivation of v2 = u2 + 2as v = u + at
v2 = (u + at)2
( ut + 1 __
2 at2 14 FUSION
v2 = u2 + 2a(s) v2 = u2 + 2as
(equation 1) (square both sides)
v2 = u2 + 2uat + a2t2 (multiply out the brackets) v2 = u2 + 2a
