First slide
Instantaneous velocity
Question

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xP(t)=at+bt2and xQ(t)=ft-t2 . At what time do the cars have the same velocity?

Moderate
Solution

Position of the car P  at any time  t, is 

xp(t)=at+bt2

vP(t)=dxP(t)dt=a+2bt……….(1)

 Similarly, for car Q

xQ(t)=ft-t2

vQ(t)=dxQ(t)dt=f-2t…….(2)

vP(t)=vQ(t)(given)

 

a+2bt=f-2t or, 2t(b+1)=f-at=f-a2(1+b)

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