Equations of Motion?

Question

s=ut+1/2at^2

When s=250, u=30 and a=-1.8, can you give me a step by step translation to calculate t. I can't remember for the life of me how to do it.

Thanks

Answer 1

s     =         ut      +          0.5 a t^2

250 =         30t     +         (0.5)(-1.8)(t^2)

250 =         30t     -           0.9 t^2

So this gives you a quadratic equation. And when you send everything to the L.H.S, you get;

0.9t^2 - 30t  + 250  = 0

Using the formula  t = ( -b +/- (b^2  - 4ac)^0.5) / 2a ;

        t = { 30 +/- ( [30^2]  - [4*0.9*250] )^ 0.5 } / { 2 * 0.9 }

      

          = 16.67 s

Answer 2

Substitute the known quantities:

250 = 30t - 0.9t²

Re-arrange:

0.9t² - 30t +250 = 0

and you have  quadratic equation

9t² - 300t + 2500 = 0

which seems to be (3t - 50)² = 0

hence 3t = 50 or t = 16.6667, unless my maths is wrong.

Answer 3

length,s=250;

initial velocity,u=30;

acceleration is -1.8

s=ut+1/2at^2

=> 1/2at^2+ut-s=0

now put the values

=> 1/2*-1.8*t^2+30*t-250=0

=>-0.9t^2+30t-250=0

now it is a quadratic equation.

so

t= 16.666667

          

Answer 4

s=ut+1/2at^2

therefore      s -1/2at^2 = ut

therefore     ( s -1/2at^2) / u = t

Then plug the figures in

Bloody rusty though!!!