Question

Two buses of equal 5 m lengths are moving with the same velocity in the same direction on a highway. The first bus is 40 m ahead of the second bus. The driver of the second bus thinks to overtake the first bus and gives an acceleration of 1 ms–2 to the bus. After what time the second bus just passes the first bus?

Answer 1

After 9.49 s second bus just passes the first bus .

Length of buses , l = 5 m .

Distance between the buses , d = 40 m .

Now , both the buses are travelling with same velocity .

Therefore , relative velocity of both the buses w.r.t each other is zero .

Now , bus accelerate with , $a=1\ m\ s^{-2}$ .

Applying equation of motion :

$s=ut+\dfrac{at^2}{2}$

Here , u = 0 m/s .

$s=\dfrac{at^2}{2}$

Putting , s = 40+5 m = 45 m ( because bus will overtake therefore add 5 m extra )

$t=\sqrt{\dfrac{2s}{a}}\\\\t=\sqrt{\dfrac{2\times 45}{1}}\\\\t=9.49\ s$

Hence , this is the required solution .

Learn More :

Kinematics

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