Question

11. A man stands at a distance'd' m behind a bus which moves forward with a constan acceleration 'a'. He starts running at a constant speed 'y' m/s. The minimum speed of the passenger so that he can catch the bus is a. 2ad m/s b. V(2ad)m/s c. ad/2 m/s d. ad m/s​

Answer 1

Answer:

method is to assume that the event (catching the bus) happened at time t. Solve for t and find the condition that t is not a real value.

Let the passenger catches the bus after time t. Distance travelled by the bus in time t.

s=0+12at2=12at2 ...(i)

Distance travelled by the passenger, s2=vt+0=vt ...(ii)

The passenger will catch the bus if, d+s1=s2

or, d+12at2=vtor12at2−vt+d=0

or, t=v±v2−2ad−−−−−−−√a

The passenger will catch the bus it t is real, i.e., v2≤2adorv≥2ad−−−√. Thus, minimum speed or passenger for catching the bus is 2ad−−−√.