Question

Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X _{ P }( t )=\alpha t +\beta t ^2$ and $X _{ Q }( t )= ft - t ^2$. At what time, both the buses have same velocity?

• A. $\frac{\alpha- f }{1+\beta}$
• B. $\frac{\alpha+f}{2(\beta-1)}$
• C. $\frac{\alpha+ f }{2(1+\beta)}$
• D. $\frac{f-\alpha}{2(1+\beta)}$

Answer 1

Answer: (D)

$X_{P}(t)=\alpha t+\beta t^{2}$
$X_{Q}=f t-t^{2}$
$V_{P}(t)=\alpha+2 \beta t$
$V_{Q}=f-2 t$
$V_{P}=V_{Q}$
$\alpha+2 \beta t=f-2 t$
$t=\frac{f-\alpha}{2 \beta+2}$