Answer:
Step-by-step explanation:
Let's first convert the speeds of the trains from km/hr to m/s:
Train A: 24 km/hr = (24 x 1000) / (60 x 60) = 6.67 m/s
Train B: 48 km/hr = (48 x 1000) / (60 x 60) = 13.33 m/s
Now, let's find the distance covered by train A until it reaches its constant speed:
v = u + at
where
u = initial velocity = 0
a = acceleration = 1/6 m/s^2
t = time taken to reach constant speed
At constant speed, v = 6.67 m/s
So, 6.67 = (1/6)t + 0
t = 40 seconds
Using the formula for distance covered during uniform acceleration:
s = ut + (1/2)at^2
The distance covered by train A during the acceleration phase is:
s = (1/2)(1/6)(40^2) = 133.33 m
Now, let's find the equation of motion for train B:
s = ut + (1/2)at^2
where
u = initial velocity = 0
a = acceleration = 1/3 m/s^2
t = time taken to overtake train A
At the time of overtaking, both trains will cover the same distance. Let's call this distance "d". So we have:
d = 133.33 + 6.67t (distance covered by train A + distance covered by train B)
Setting the equations for both trains equal to each other, we get:
133.33 + 6.67t = (1/2)(1/3)t^2 + (1/3)t^2
Simplifying and solving for t, we get:
t = 180 seconds
Therefore, train B will overtake train A after 180 seconds or 3 minutes.