student is standing at distance of 50 m from the bus.As soon as the bus begins its motion with an acceleration of 1m/s^2, the student starts running towards the bus with a uniform velocity u.assuming that the motion is along the straight road,find the minimum value of u the boy should attain to catch the bus .

If the student catches the bus in time t, then the distance travelled by the bus,

 

S_b = 1/2 a t² and the student,S_s = ut

 

Suppose the initial differnce between the two is d,

 

S_s = S_b+d

 

t =  (u +/- sqrt( u² - 2ad))/a

 

The student will be able to catch the bus, if the time is real,

 

if u² >= 2ad

 

d = 50m/s

 

u>=10m/s