Twocars start together in the same direction from the same place. The first goes with uniform speed of 10km/hr. The second does at a speed of 8km/hr in the first hour and then increases its speed by ½ km in each succeeding hour. After how many hours will the second overtake first if both goes non stop.

Lets solve this in the frame of reference of the 2^nd car
we look at the parameters of the car
u = -2km/hr
a = 0.5km/hr2
and we want to find where the displacement becomes zero
s = 0
so by 2^nd equation of kinematics

t = 8hrs

Dear Student,

If you observe, the first person covers 10km in each hour. That means after n hours, first one will cover total 10n km of distance.

Now coming on to the second one, He covers 8 km in first, 8 + ½ km in second, 8 + ½ +1/2 km in third and so on. this forms and A.P with a = 8, d = ½. So the toal distance travelled by second at the end of n hours is the summation of the series upto n terms.
Calculate it, you will get n/2(16+(n-1)1/2).
Equate it with 10n and get the value of n as your answer.

Thanks.