JEE Mains · Physics · STD 11 - 2. motion in straight line
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 \(x_Q(t)= ft- t^2\). At what time do the cars have the same velocity \(?\)
- A \(\frac{{a + f}}{{2\left( {1 + b} \right)}}\)
- B \(\;\frac{{f - a}}{{2\left( {1 + b} \right)}}\)
- C \(\;\frac{{a + f}}{{\left( {1 + b} \right)}}\)
- D \(\;\frac{{a + f}}{{2\left( {b - 1} \right)}}\)
Answer & Solution
Correct Answer
(B) \(\;\frac{{f - a}}{{2\left( {1 + b} \right)}}\)
Step-by-step Solution
Detailed explanation
\begin{array}{l} \,\,\,Position\,of\,car\,P\,at\,any\,time\,t,\,is\\ \,\,{x_p}\left( t \right) = at + b{t^2}\\ \,\,{v_p}\left( t \right) = \frac{{d{x_p}\left( t \right)}}{{dt}} = a + 2bt\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\…
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