A passenger is standing ‘d’ m away from a bus. The bus being to move with constant acceleration a. To catch the bus, the passenger runs at a constant speed v towards the bus. What must be the minimum speed of the passenger so that he may catch the bus?
Let the passenger catch the bus after time t. From 2nd equation of motion, the distance travelled by the bus,
and the distance travelled by the passenger
s2 = ut + 0 …(2)
Now the passenger will catch the bus if
d + s1 = s2 …(3)
Substituting the values of s1 and s2 from Eqns. (1) and (2) in (3), we get
So the passenger will catch the bus if t is real, i.e.,
So the minimum speed of passenger for catching the bus is
A person walks up a stalled escalator in 90 second. When standing on the same escalator, now moving he is carried up in 60 second. How much time would it take him to walk up the moving escalator?
The driver of a train moving at a speed v1 sights a goods a train a distanced ahead of him on the same track moving in the same direction with a slower speed v2. He Puts on a brakes and gives his train a constant retardation a. Show that there will be no collision if