The speed of sound in a medium depends on the modulus of elasticity $E$ and density $\rho$ of the medium. Using dimensional analysis, determine the relationship between these quantities.

In ${\rm{\;S}} = a + bt + c{t^2}$. S is measured in metre and t in second. The unit of c is

Which of the following equations is dimensionally consistent? (Where 'v' is velocity, 'u' is initial velocity, 'a' is acceleration, and 't' is time)

The velocity of a particle (v) at an instant t is given by $v = at + b{t^2}$ the dimension of b is

The velocity of a particle (v) at an instant t is given by $v = at + b{t^2}$ the dimension of b is