Question

Two cars A and B are moving with 50 m/s velocity. Car A is initially 100m ahead of B. If driver of Car B accelerates it by 2 m/s^2 , how much time is required for Car B to overtake Car A

Answer 1

Solution :
Let the time taken by car B to Overtake Car A = t
  Therefore the total distance  Car B has to travel = Initial Distance (100 m) + distance travelled by Car A in t sec
                         Distance Traveled by Car A in t sec = velocity of  Car A * t (Because  velocity = distance / time ) .
                                       = 50t
Therefore the total distance  Car B has to travel = 100 + 50t.
We know that ,
     S = ut + 1/2at^2
   u=velocity of car B and a= accelaration Of car B
100 + 50 t = 50 t + 1/2 * 2* t^2

100 = t^2
=> t^2 = 10 ^ 2
=> t = 10 sec .
hence The time taken by the car B to overtake Car A  = 10 seconds

                                                            

Answer 2

B..................................A...........................................
<----------------------------------><------------------------------------------>
     100m                                  s
let car A travail s meter in time t , then
s = 50t  ..................(1)
car B travail (s +100) meter in time t
s+100 = 50t + 1/2*2*t^2  ..............................(2)
put the value s from equation (1)
50t + 100 = 50t + 1/2*2*t^2
t^2 = 100
t = 10 or -10
since time can not be negative ,so 
t = 10Sec.