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Two cars start off to race with velocities 4m/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 same time, then the length of path is

$(a)\; 30 m \quad (b)\;32 m \quad (c)\;20 m \quad (d)24 m$

$s=4t+\large\frac{1}{2}$$(1)t ^2 \quad=2t+\large\frac{1}{2}$$(2)t^2$
$=>t=0\;or\;t=4s$
Therefore $s=4 (4)+\large\frac{1}{2}$$(1) 4^2$
$=24m$
Hence d is the correct answer
edited May 23, 2014