Question

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $X_{P}\left(t\right)=at+bt^{2}$ and $X_{Q}\left(t\right)=ft-t^{2}$ . At what time do the cars have the same velocity?

• A. $\frac{a - f}{1 + b}$
• B. $\frac{a + f}{2 \left(b - 1\right)}$
• C. $\frac{a + f}{2 \left(1 + b\right)}$
• D. $\frac{f - a}{2 \left(1 + b\right)}$

Answer 1

Answer: (D)

$v_{P}=\frac{d X_{P}}{d t}=a+2bt$
$v_{Q}=\frac{d X_{Q}}{d t}=f-2t$
Now for, $v_{P}=v_{Q}$
$\Rightarrow a+2bt=f-2t$
$\Rightarrow 2t+2bt=f-a$
$\Rightarrow t=\frac{f - a}{2 \left(\right. b + 1 \left.\right)}$