A car and a bus is running along the same straight road at 54km/hr and 36 km/hr . if the bus is 0.5 km ahead of the car , calculate the time taken by the car to overtake the bus?
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The car B will catch car A after 12 minutes and at the distance of 15 km.
Explanation:
Given that,
Speed of car A = 60 km/hr
Speed of car B = 70 km/hr
Distance d = 2.5 km
Acceleration of car B a = 20 km/hr^2a=20km/hr
2
Let us consider car A moves at time t.
The distance of car A is
s_{A} = 60 ts
A
=60t
The distance of car B is
Using equation of motion
s = ut+\dfrac{1}{2}at^2s=ut+
2
1
at
2
s_{B}= 70t+10t^2s
B
=70t+10t
2
The time is
s =s_{B}-s_{A}s=s
B
−s
A
2.5 = 70t+10t^2-60t2.5=70t+10t
2
−60t
2.5= 10t+10t^22.5=10t+10t
2
10t^2+10t-2.5= 010t
2
+10t−2.5=0
t = 12 mint=12min
The distance of car B is
s_{B}= 70\times 0.21+10(0.21)^2s
B
=70×0.21+10(0.21)
2
s_{B} = 15 kms
B
=15km
Hence, The car B will catch car A after 12 minutes and at the distance of 15 km.
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