Question

If relation between distance and time is $s=a+bt+c{t}^2,$ find initial velocity and acceleration :

• A. $b+2ct,2c$
• B. $b,2c$
• C. $2c,b$
• D. $b+2c,2c$

Answer 1

Answer: (B)

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