
If the velocity v of a particle moving along a straight line decreases linearly woth its displacement s from 20 metre per second to a value approaching zero at s=30 metre, then acceleration of the particle at s =15 metre is ...

The horizontal and vertical distances traveled by a particle in time t are given by x = 6t and y=8t5t^2 . If g=10m/sec^2 , then the initial velocity of the particle is a) 8 m/sec b) 10 m/sec c) 5 m/sec d) zero ...

The velocitytime graph of a body is shown in figure. The displacement covered by the body in 8 seconds is *Image* a) 10 m b) 9 m c) 24 m d) 30 m ...

One of the rectangular components of a vector of magnitude 100 units is 50 units. Find the other component. ...

A river flows downstream with a speed of 8 km/h and the velocity of the swimmer with respect to the water is 6 km/h. Find out the minimum time taken to reach the other side of the bank.What is the displacement of the man down ...

Show that the velocity is perpendicular to the displacement, if r = A Cos Ï‰t (i^) + A Sin Ï‰t (j^) ...

Assuming the mass 'm' of the largest stone that can be moved by a flowing river depends upon the velocity 'v' of water,density 'd' of water and acceleration due to gravity 'g'. Show that 'm' varies as the sixth power of the v ...

A block of mass m is attached to one end of a long elastic rope. The other end of the elastic rope is fixed to the roof of a building. Initially the block is in contact with the roof at the point where the rope is fixed and i ...

*Image* ...

A particle located at x=o at time t=0 starts moving along the positive Xdirection with a velocity v that varies with time is? explain ...

A gun is fired from a moving platform and the range of the shot is R when the platform is moving forward and S when the platform is moving backward. The velocity of the shot is V. Prove that the gun is elevated at an angle ta ...

Three identical spheres of mass 1 kg are placed touching each other with their centers on a straight line. Their centers are marked K,L and M respectively. What is the distance of the center of mass of the system from K? ...

Two point masses m and M are separated by a distance L. What is the distance of the center of mass of the system from m? ...

A 60kg body is pushed with enough force to start it moving across a floor and it continues to act afterwards. The coefficient of static friction is 0.5 and the coefficient of sliding friction is 0.4 . Calculate the accelerati ...

A particle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum,calculate the radial force acting on the particle. ...

A particle moves along a circle of radius (20/Ï€)m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun,what is the tangential acceleratio ...

A motorcyclist starts from the bottom of a slope of angle 45Â° to cross a valley. The width of the valley 90m and length of the slope is 80 2 m. What is the minimum value of u (initial velocity)? ...

A cannon ball is fired with a velocity v such that it makes an angle Î¸ with the horizontal. At the highest point,the cannon ball splits into two parts of equal masses. One of the parts retraces the initial path of the ball. ...

A rod of length 10 m. is travelling on a smooth,level,horizontal surface.Beyond a point A,the floor ceases to be smooth and the coefficient of friction is k=0.1.The rod is travelling such that it is moving towards the point A ...

A particle is projected from the bottom of an inclined plane at an angle Î¸ with the surface of the incline.The angle of the inclined plane is 45.For what value of Î¸ will the particle retrace it's path after collision with t ...

The secondâ€™s hand of a watch has length 6 cm. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be a) 6.28 and 0 mm/s b) 8.88 and 4.44 mm/s c) 8.88 and 6.28 mm/s d) 6.28 and 8. ...

A particle is projected from the origin in such a way that it passes through a given point P(a,b). What is the minimum speed required to do so? ...

A particle is projected from a point A,whose position vector is 2i + 3j,with initial velocity vector 20i + 30j + 20k,where i and k are horizontal and j is the unit vector in the direction of the upwards vertical. Find a vecto ...

A ball is dropped from the top of a building at t = 0. At a later time t = t0,a second ball is thrown downwards with initial speed v0. Using relative motion concept, find the time at which the two balls will meet. ...

If R be the range of a projectile on horizontal plane, and H1 and H2 be the maximum heights for its two possible trajectories,find the relation between the given parameters. ...

The velocity of a train increases at a constant rate Î± from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate Î². If x be the total distance covered,find the total time take ...

Two particles move in an uniform gravitational field with acceleration g. Initially the particles were located at one point and moved with velocities v1 = 3m/s and v2 = 4m/s horizontally in opposite directions. Find the dista ...

A marble rolls off horizontally from the edge of the table and lands on the floor. 1)How long does the marble take to reach the floor? 2)At what horizontal distance from the edge of the table does the marble land? 3)What is t ...

In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If {{a}_{0}} is the radius of the ground state orbit, m is the mass, e is the charge on t ...

A particle is projected with velocity 2âˆš(gh) so that it just clears two walls of height h which are at a distance of 2h apart from each other. Prove that the time of passing between the two walls is 2âˆš(h/g). ...