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Two cars start off to race with velocities 4 m/s and 2 m/s and travel in straight line with uniform acceleration 1 $m / s^{2}$ and $2 m / s^{2}$ respectively. If they reach the final point at the same instant, then the length of the path is

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30 m

32 m

20 m

24 m

answer is D.

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Detailed Solution

$s = 4 t + \frac{1}{2} (1) t^{2} = 2 t + \frac{1}{2} (2) t^{2}$

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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