If x = a + bt + c${{t}^{2}}$, where x is in metre and t in seconds, what is the unit of c?



The unit of left hand side is metre so the units of c${{t}^{2}}$ should also be metre. Since ${{t}^{2}}$ has unit of ${{s}^{2}}$, so the unit of c is m/${{s}^{2}}$