Question

supposse the displacement of a particle is related to a time according to expression S=ct3 what are the dimension of c constant

Answer 1

S = displacement = [ L¹ ]
t  = time = [ T¹ ]
c = S/t³ 
   = [ L¹ ] / [ T¹ ]³
   = [ L¹ ] / [ T³ ]
   = [ L¹ T⁻³ ]
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Answer 2

S = Ct³
where S is displacement of particle
t is time taken by particle

dimension of S = [ L ]
dimension of t = [ T ]

now,
dimension of S = dimension of C × { dimension of t}³
[ L ] = dimension of C × [ T ]³
dimension of C = [ L ] /[ T ]³
dimension of C = [ L T -³ ]