Question

Two cyclists start together in the same direction from the same place . the first goes with uniforn speed of 10 km per hour . the second goes at a speed of 8km per hour in the first hour and increases the speed 1/2 km each succeeding hour. after how many hours the second cyclist overtake the first f both go non-stop

Answer 1

The first cyclist moves at 10km/hr.
Second moves at 8km/hr.
So the relative initial velocity is 2km/hr
(since both move in same direction)

Relative accln b/w them is -0.5km/hr^2

Let the relative distance between them becomes zero after t hr.
0=(2)t-0.5(0.5)(t^2)
t= 8 hr.
So the second cycle overtakes first after 8hours