Starting from the origin at time t = 0 , with initial velocity 5 ⏜...

Starting from the origin at time

\text{t} = 0

, with initial velocity

5\overset{⏜}{j}\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm{ms}^{-1}

, a particle moves in the

x

y

plane with a constant acceleration of \left(10\overset{⏜}{i} + 4\overset{⏜}{j}\right){ms}^{- 2}

. At time

\text{t}

, its coordinates are \left(20{m, y}_{0}\text{m}\right)

. The values of

\text{t} and {y}_{0}

are, respectively:

Options

A $2\text{s}$ and $18\text{m}$
B $4\text{s}$ and $52\text{m}$
C $2\text{s}$ and $24\text{m}$
D $5\text{s}$ and $25\text{m}$

Correct answer

A. $2\text{s}$ and $18\text{m}$

Step-by-step solution

Equation $\left(1\right)$

${S}_{x} = \dfrac{1}{2}{a}_{x}{t}^{2}$

$20 = \dfrac{1}{2} \times 10 \times {t}^{2}$

$t = 2$

Equation \left(2\right) $$ {S}_{y} = {u}_{y}t + \dfrac{1}{2}{a}_{y}{t}^{2} $$ y = 5\left(2\right) + \dfrac{1}{2}\left(4\right){\left(2\right)}^{2} $$ y = 18

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