Statics and Dyn...

The displacement of a particle at time t is x , where x = t ⁴ - kt ³ . If the velocity of the particle at time t = 2 is minimum , then

The displacement x of a particle at time t is given by x = At ² + Bt + C, where A, B and C are constants and v is velocity of a particle, then the value of 4Ax - v ² is

The velocity of a particle at time t is given by the relation v = 6t - t ² / 6. The distance travelled in 3 s is, if s = 0 at t = 0

A particle moves in a straight line so that it covered a distance (at ³ + bt + 5) m in t s (g = 32 ft/s² ). If its acceleration after 4 s is 48 m/s² , then a is equal to

A train of length 200 m, travelling at 30 m/s overtakes another train of length 300 m, travelling at 20 m/s in the same direction. The time taken by the first train to pass the second is

The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8 m/s². The time taken by the particle to move the second metre is

Two stones A and B are thrown at an angle of 50° from the horizontal. The velocity of B is twice of the velocity of A. The ratio in the greatest heights attained by A and B is

A particle is projected vertically upwards and is at a height h after t₁ sec and again after t₂ sec, then

If a falling body covers 75 m in its last second, then the height (in metres) from which it is falling, is (take g = 10 m/s²)