Question

A student is standing at a distance of 50 m from the bus as soon as the bus begins its motion with an acceleration of 1 M per second the stuudent starts running towards the Bus with uniform velocity U asuming the motion to be along straight road the minimum value of u so that the student is able to catch the bus is

Answer 1

To catch the bus, their distance covered should be same in same time.
For bus let it covered x distance from initial position.
s=ut+1/2at²
therefore,

x = 0 + 0.5*1*t²
x = t²/2 ….............................................(1)

For student,
(x + 50) = u*t........................................(2)
substituute eq. (1) from eq. (2)
t²/2 + 50 = ut
or
u = t/2 + 50/t
du/dt = ½ – 50/tt = 0
50/t² = 0.5
t² = 50/0.5 = 100
t = 10 seconds u = 10/2 + 50/10
= 5 + 5
= 10 m/s