 Physic college
posted by meera .
The equation for the change of position of a train starting at x
= 0 is given by
x=1/2at^2 + bt3 . Find the dimensions of a and b.
If y = C1 sin (C2 t)
where y is a distance and t is the time. What are the dimensions of C1 and
C2 ?.

x=1/2 a t^2 + bt^3
if at^2 is distance, then a must be distance/time^2
b has to be distance per time^3
If y is distance, C1 must be distance. C2 must be 1/time 
if at^2 is distance, then a must be distance/time^2
okay but from where can i get distance ?!
i mean as a number !
also here sin (C2 t) i think it is constant so we can't take dimension or i am wrong :(
Again Thank u a lot :D 
You are solving dimensional analysis here, just the dimensions. There are no numbers.
The argument in a trig function is in radians, So C2*time must divide out all units, so C2 is 1/time. 
should we divied it , I mean solve it like
x = 1/2at^2 ,x= bt^3 and take each part individual !
how can get red of (sin) from this formula ,
also here should i handle it individual ! 
af