Two cars P and Q starts from a point at the same time in a straight line and their positions are represented by xp(t)=at+bt2 and xQ(t)=ft−t2. At what time do the cars have the same velocity?
Position of car P,
xp(t)=at+bt2
Thus, velocity of car P
vp=d[xp(t)]dt=a+2bt
Position of car Q
xQ(t)=ft−t2
Thus, velocity of car Q
vQ=d[xQ(t)]dt=f−2t
According to the question,
vp∣∣∣t=to= vQ∣∣∣t=to
∴a+2bto=f−2to
⟹to=f−a2(1+b)