# 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

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by Blacksheep

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by Blacksheep

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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

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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.