If the equation for the velocity of a particle at time ' $t$ ' is $v=$ at $+\frac{b}{t+c}$, then the dimensions of $a, b, c$ are respectively

If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively, then $\sin ^2 \alpha+\sin ^2 \beta=$

A particle moving along a straight line covers the first half of the distance with a speed of $3 \mathrm{~ms}^{-1}$, the other half of the distance is covered in two equal time intervals with speeds of $4.5 \mathrm{~ms}^{-1}$ and $7.5 \mathrm{~ms}^{-1}$ respectively, then the average speed of particle during the motion is