Miscellaneous T...

If a particle has two velocities each equal to u in magnitude and their resultant is also of magnitude u, then the angle between the two velocities is

If two velocities u and v are inclined at such an angle that the resultant of 2u and v inclined at the same angle is at right angle to v, then the resultant of u and V is of magnitude

If a particle having simultaneous velocities 3 m/sec, 5 m/sec. and 7 m/sec. at rest, then the angle between the first two velocities is

The greatest and least magnitudes of the resultants of two velocities of constant magnitudes are ii and v respectively. If a particle has these velocities inclined at an angle 2a, then the resultant velocity is of magnitude

If the distance S covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

The average speed of a bicycle over a journey of 20 km; if it travels the first 10 km at 15 km/hr and the second 10 km at 10 km/hr, is

If OP makes 4 revolutions in one second, the angular velocity in radians per second is

A velocity 1/4 m/s is resolved into two components along OA and OB making angles 30^o and 45° respectively with the given velocity, then the components along OB is

Two straight railways converge to a level crossing at an angle x and two trains are moving towards the crossing with velocities u and v. If a and b are the initial distances of the trains from the crossing, the least distance between them will be after time t given by

The velocity v of a particle is at any time related to the distance travelled by the particle by the relation v = as + b, where a > 0 and b ≤ a/2. Which of the following statements will be true for this motion (Given s = 0 when t = 0)?