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 $-10,-33$

When the particle comes to rest, then its velocity is zero. The velocity of the particle is,
$\frac{ds}{dt}=2t+a$
At $t=5$ sec
$0=2\times 5+a$
$\Rightarrow a=-10$

And at $t=5$ sec, distance, $s=25$
Substitute the values in the equation, $s=t^2+at-b+17$
$25=5^2+(-10)\times 5-b+17$
$\Rightarrow b=-33$