s = ut + 1/2 at sqaured?

Question

how do i transpose the formulae make 'a' the subject

cheers

Answer 1

This is a basic physics question concerning distance travelled after a period of acceleration. u is the starting velocity, t is time and 'a' the acceleration. If the starting velocity is zero then 'ut' is zero and can be ignored. When starting at zero velocity the distance is half x acceleration x time squared. This means the acceleration 'a' equals 2s/t^2.

If the starting velocity is not zero then you need to add the extra term -2u/t.

This can be shown as:

s = ut + (at^2)/2
s -ut = (at^2)/2
2s - 2ut = at^2
Turning this around and dividing both sides by t^2, then:
a = (2s - 2ut)/t^2
expanding out the bracket gives:
a = 2s/t^2 -2u/t

I don't think you should believe engineers, even if they do use it on a daily basis. Leave it to the physicists - a dying breed!

Answer 2

s = ut + 1/2at^2
s - ut = 1/2 at^2
2(s-ut) = at^2
2(s-ut)/t^2 = a transposing

a = 2(s-ut)/t^2

Answer 3

s-ut = at^2/2
2(s-ut)/t^2 = a

Answer 4

The correct answer to make the A the subject is:

a= (s/0.5t^2)-(ut)

Trust me im an engineer and use it everyday.

Answer 5

2*(s - ut)/(t^2) = a