A body starts from the origin with an acceleration of $6 m s^{- 2}$ along the $x$ -axis and $8 m s^{- 2}$ along the $y$ -axis. Find its distance from the origin after $4$ s.

80 m

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70 m

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60 m

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90 m

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Solution

The correct option is B $80 m$
Displacement along $X$ -axis:
$x = u_{x} t + \frac{1}{2} a_{x} t^{2} = \frac{1}{2} \times 6 \times (4)^{2} = 48 m$
Displacement along $Y$ -axis:
$y = u_{y} t + \frac{1}{2} a_{y} t^{2} = \frac{1}{2} \times 8 \times (4)^{2} = 64 m$
Total distance from the origin
$= \sqrt{x^{2} + y^{2}} = \sqrt{(48)^{2} + (64)^{2}} = 80 m$

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