## Question

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?

### Solution

Let the passenger catch the bus after time *t.* From 2^{nd} equation of motion, the distance travelled by the bus,

and the distance travelled by the passenger

*s*_{2} = *ut* + 0 …(2)

Now the passenger will catch the bus if

*d* + *s*_{1} = *s*_{2} …(3)

Substituting the values of *s*_{1} and *s*_{2} 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

#### SIMILAR QUESTIONS

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 *v _{1}* sights a goods a train a distance

*d*ahead of him on the same track moving in the same direction with a slower speed

*v*

_{2}. He Puts on a brakes and gives his train a constant retardation a. Show that there will be no collision if