Volume 1

A swimmer crosses a flowing stream of width ω to and fro in time t1. The time taken to cover the same distance up & down the stream is t2 . if t3 is the time swimmer would take to swim a distance 2ω in still water, then: Two particles are moving with velocities v1 [...]

A glass wind screen whose inclination with the vertical can be changed is mounted on a car. The car moves horizontally with a speed of 2m/s. At what angle α with the vertical should the wind screen be placed so that the rain drops falling vertically downwards with velocity 6m/s strike the wind screen perpendicularly? [...]

Two particles start moving from the same point along the same straight line. The first moves with constant velocity v and the second with constant acceleration a. During the time that elapses before the sound catches the first, the greatest distance between the particle is. A car starts moving along a line A sphere of [...]

The 1/v versus positions graph of a particle is shown in the figure, where v is the velocity of the particle. The particle is moving in a straight line along positive x- axis. Find the time taken by the particle to reach from the point A to B in second. The 1/v versus positions graph [...]

Figure shows the velocity time graph for a particle travelling along a straight line. The magnitude of average velocity (in m/s) of particle during the time interval from t = 0 to t = 6s is 10α. Find the value of α. A car starts moving along a line A sphere of mass 10 kg [...]

A ball is thrown upwards with a speed of 40m/s. When the speed becomes half of the initial speed, gravity is switched off for next 2 second. After that gravity is again switched on but magnitude gravity is doubled. The total distance travelled by the ball from t=0 to the time when the ball reaches [...]

A particle is moving with velocity (2i+3j) m/s from a point (4,5) m. At time same instant a particle B, moving in the same plane with velocity (4i + j) m/s passes through a point C(0, -3)m. Find the x – coordinate (in m) of the point where the particles collide. -3)m. Find the x [...]

Two particles are moving with velocities v1 = i – tj + k and v2 = ti + tj + 2k m/s respectively. Time at which they are moving perpendicular to each other is ……..(second) Two particles are moving with velocities v1 = i - tj + k and v2 = ti + tj + [...]

The diagram shows the variation of 1/v (where v is velocity of the particle) with respect to time. At time t = 3 s using the details given in the graph, find the instantaneous acceleration (in m/s^2) find the instantaneous acceleration (in m/s^2) The diagram shows the variation of 1/v (where v is velocity of [...]

A lift performs the first part of its ascent with uniform acceleration, a, and the remaining with uniform retardation, 2a. If, t, is the time of ascent, the depth of the shaft is at^2/n. Find value of n. 2a. If A lift performs the first part of its ascent with uniform acceleration A) and the [...]