Question

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

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

Answer 1

Answer: (D)

$\frac{f - a }{2( 1 + b)}$

Answer 2

$v_{p} = \frac{dx_{p}}{dt} = a +2bt$ $v_{Q} = \frac{dx_{Q}}{dt} = f - 2t$ $v_{P} = v_{Q} \Rightarrow a +2bt =f-2t$ $t =\frac{ f-a}{2\left(b+1\right)}$