Question

A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time $t$ is given by $s=t^2+at-b+17$, where $a$ and $b$ are real numbers. If the particle comes to rest after $5s$ at a distance of $s=25$ units from the fixed point, then value of $a$ and $b$ are respectively.

• A. $10,-33$
• B. $-10,-33$
• C. $-8,33$
• D. $-10,33$

Answer 1

The correct option is B $-10,-33$

Given,

$s=t^2+at-b+17$

After $5s$,

${\left[\frac{ds}{dt}\right]}_{t=5}=[2t+a{]}_{t=5}=0$

$\Rightarrow a=-10$

At $t=5s,s=25$ units

$\therefore 25=5^2+5a-b+17$ $[\because s=25$ and $t=5]$
$\Rightarrow 25=25+5(-10)-b-b+17$
$\Rightarrow 50-17=-b$
$\Rightarrow b=-33$