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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.

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.

Grade:8

2 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
Lets solve this in the frame of reference of the 2nd 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 2nd equation of kinematics
0 = -2t + t^2/4
t = 8hrs
Vijay Mukati
askIITians Faculty 2590 Points
5 years ago
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.

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