Question

Two stones are thrown vertically upwards simultaneously with their initial velocities u₁ and u₂ respectively. Prove that the heights reached by them would be in the ratio of u₁² : u₂² (Assume upward acceleration is –g and downward acceleration to be +g).

Assertion (A): If the velocity of a body in uniform motion changes, its acceleration cannot remain constant. Reason (R): If a body is thrown vertically upward, the relationship between initial velocity (u) and acceleration (a) at any moment is v² – u² = 2as.

An aeroplane requires a minimum speed of 360 km h⁻¹ for its take off from a runway. If the aeroplane engine can produce a maximum acceleration of 10 m s⁻² during its motion on runway, what should be the minimum length of runway for a successful take off by the aeroplane?

A charged particle travels longitudinally inside a straight hollow tube of 2 m length with a uniform acceleration. If the particle enters the tube with a velocity of 1000 m s⁻¹ and leaves at 9000 m s⁻¹, what is the acceleration of the particle? For how long is the charged particle in the tube?

A vehicle travelling with uniform acceleration crosses two points A and B with speeds of 20 m s⁻¹ and 30 m s⁻¹ respectively. With what speed does the vehicle cross the midpoint of A and B?