A stone falls freely under gravity. It covers distances h₁, h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h₁ and h₂ and h₃ is

The motion of a particle along a straight line is described by equation x = 8 + 12t − t³ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is

A ball is dropped from a high rise platform at 1 = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v?

(Take g = 10m∕s²)

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S₁ and that covered in the first 20 seconds is S₂, then

A ball is projected with a velocity, 10ms⁻¹, at an angle of 60^∘ with the vertical direction. Its speed at the highest point of its trajectory will be

The speed of a swimmer in still water is 20m∕s. The speed of river water is 10m/s and is flowing due east.

If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given by

Two particles A and B are moving in uniform circular motion in concentric circles of radii r_A and r_B with speed v_A and v_B respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be

The x and y coordinates of the particle at any time are x = 5t − 2t² and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s

If vectors  are functions of time, then the value of t at which they are orthogonal to each other is