Rectilinear Motion

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Question

Two cars start off to race with velocities 4 m/s and 2 m/s and travel in straight line with uniform accelerations 1 m/ $s^{2} a n d 2 m / s^{2} r e s p e c t i v e l y$ . If they reach the final point at the same instant, then find the length of the path (in meter).

Moderate

Solution

$s = 2 t + \frac{1}{2} (2) t^{2}$ =4t+ $\frac{1}{2} . 1 . t^{2}$
or $4 t + 0 .5 t^{2} = 2 t + t^{2}$
or $\frac{t^{2}}{2} = 2 t or t = 0 and t = 4 s$
$s = (4) (4) + \frac{1}{2} (1) (4)^{2} = 16 + 8 = 24 m$

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