Question

S = ut + (at² × 1/2)
Make t the subject

Answer 1

Answer:

As suggested, you can use the quadratic equation here.

From the equation (which I will just write for reference).

s=ut+12at2

Move all the variables to one side of the equal side sign.

at22+ut−s=0

Now from the quadratic equation (which I will again write for reference).

x=−b±b2−4ac√2a

Then the variables for the quadratic equation are.

a=a2

b=u

c=−s

This looks strange as one of the variables, a, for the quadratic equation and the equation of motion are the same so just try to keep this in mind.

Now substitute and of course change the subject to the variable t.

t=u±u2−(4×12a×−s)√a

t=−u±u2+2as√a

Here we have the formula with the subject t .

In case you want another method, you can do so by completing the square.

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You can start by factorising a2

s=a2(t2+2ua)

Now complete the square.

s=a2(t2+2ua+(ua)2)−(ua)2(a2)

Then using (a+b)2=a2+2ab+b2

s=a2(t+ua)2−u22a

Then add both sides by u22a

s+u22a=a2(t+ua)2

Change the variable s to a denominator of 2a by multiplying both the numerator and denominator by 2a

u2+2as2a=a2(t+ua)3

Continue to simplify.

2u2+4as2a2=(t+ua)2

Factorise two and cancel.

u2+2asa2=(t+ua)2

Then take the square root of both sides.

t+ua=±u2+2asa2−−−−−√

Then write our final answer.

t=−u±u2+2as√a

Thanks and hope I could help.