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 \( X_{Q}(t)=f t-t^{2} \). At what time, both the buses have same velocity? (1) \( \frac{\alpha-f}{1+\beta} \) (2) \( \frac{\alpha+f}{2(\beta-1)} \) (3) \( \frac{\alpha+f}{2(1+\beta)} \) (4) \( \frac{f-\alpha}{2(1+\beta)} \)

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? 

Answer 1

Correct option is (4) \(\frac{f-\alpha}{2(1+ \beta)}\)

Let t be the time when velocity becomes equal.