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Vector Addition

Two particles...

Question

Two particles one with a constant velocity 50 m/s and another starts from rest with uniform acceleration $10 m / s^{2}$ starts moving simultaneously from the same point and in the same direction at a distance 125 m. Calculate time.

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Solution

$u = - 50 m / s a = 10 m / s^{2} s = 125 m s = u t + \frac{1}{2} a t^{2} \Rightarrow 125 = - 50 t + \frac{1}{2} \times a t^{2} \Rightarrow 25 = - 10 t + t^{2}$
Solving for 't' we get,
$t = 5 + 5 \sqrt{2} = 5 (1 + \sqrt{2}) s e c o n d s$

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