Two boys are standing at the ends A and B of a ground, where `AB=a`. The boy at B starts running in a direction perpendicular to AB with velocity `v_(1)`. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is :

A body starts from rest and acquires a velocity V in a time T.The work done on the body in a time t is proportional to

A particle moves with an initial velocity v_(0) and retardation alpha v , where v is the velocity at any time t.

A body starts from rest and acquires a velocity V in time T .The work done on the body in the time t is proportional to

A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with a constant velocity u, the time of flight of the stone is :

Three particles of equal masses are placed at the corners of an equilateral triangle as shown in the figure. Now particle A starts with a velocity v_(1) towards line AB , particle B starts with a velocity v_(2) towards line BC and particle C starts with velocity v_(3) towards line CA . The displacement of CM of three particle A, B and C after time t will be (given if v_(1)=v_(2)=v_(3))

By what fraction does the mass of a boy increase when he starts running at a speed of 12 km h ^(-1)?

A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity v. The two bodies meet after a time t. The value of t is