A particle starts from origin at t = 0 with a velocity 5 ^ i m s ^...

Given, ${u}_{x} = 5m{s}^{- 1}, {a}_{x} = 3m{s}^{- 2}, x = 84m$

The formula to calculate the velocity of the particle along x-axis is given by

${v}_{x}^{2} = {u}_{x}^{2} + 2ax . . . \left(1\right)$

From equation (1), it follows that

${v}_{x}^{2} = 25 + 2 ( 3 ) ( 84 ) ⇒ {v}_{x} = 23m{s}^{- 1}$

Also, the velocity of the particle along x-axis can be written as

${v}_{x} = {u}_{x} + {a}_{x}t . . . \left(2\right)$

From equation (2), it follows that

$\begin{cases}t & = & \dfrac{23 - 5}{3} \\ & = & 6s\end{cases}$

Similarly, for the $y -$ component of the velocity, it follows that

$\begin{cases}{v}_{y} & = & 0 + {a}_{y}t \\ & = & 0 + 2 \times ( 6 ) \\ & = & 12m{s}^{- 1}\end{cases}$

Hence, the magnitude of the velocity is given by

${v}^{2} = {v}_{x}^{2} + {v}_{y}^{2} = {23}^{2} + {12}^{2} = 673v = \sqrt{673}m{s}^{- 1}$

Therefore, $\alpha = 673$.