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  4. If relation between distance and time is s=a+bt+ct2, find initial velocity and acceleration :

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Q. If relation between distance and time is $ s=a+bt+ct^2, $ find initial velocity and acceleration :

Rajasthan PMTRajasthan PMT 2006Motion in a Straight Line

Solution:

$s=a+b t+c t^{2}$
$\Rightarrow v=\frac{d s}{d t}=b+2 c t$
$\Rightarrow $ Initial velocity $=\left|\frac{d s}{d t}\right|_{t=0}=b$
and $a=\frac{d v}{d t}=2 c$
$\Rightarrow $ Initial acceleration $=\left|\frac{d v}{d t}\right|_{t=0}=2 c$