Why does integration only work. The equation of motion v=u+at gives a different answer. If given that a particle starts from rest when time t=0. It ravels with acceleration (24t-16)m/s/s. where t is time measured from the instant when the particle is at rest. find its velocity when t=3.
I know you have to differentiate to get your answer but why does it not work when I use the equations of motion: v=u+at. I get 2 completely different answers please explain. When i integrate i get v=60m/s when I use the formula I get v=168m/s. 

you get the formula $v=u+at$ when $a$ is constant but it is not the case here in your question.
let acceleration be constant
By definition
$$\frac {dv}{dt}=a$$
Seperating the variables and  integrating the above equation we get 
$$\int_{v_1} ^v dv=a\int_0 ^t dt$$
where $v_1 $ is the initial velocity
$$\implies v=v_1+at$$
So it will be wrong if you will apply the formula in the question.
Hope this helped.
