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 $a,b$ are real numbers. If the particle comes to rest after $5$ sec at a distance of $s=25$ units from the fixed point, then values 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, $s=t^2+at-b+17$

Therefore, ${\left[\frac{ds}{dt}\right]}_{t=5}=[2t+a{]}_{t=5}=0$
$\Rightarrow a=-10$
and $25=5^2+5a-b+17(s=25,t=5)$
$\Rightarrow b=-33$