The equation for the change of position of a train starting at x

Question

= 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 ?.

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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 !