The boxes of masse 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s²)

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms^-2. The gases come out at a relative speed of 500 ms^$$-$$1 with respect to the rocket : [Use g = 10 m/s²]

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

$$F = {F_0}\left[ {1 - {{\left( {{{t - T} \over T}} \right)}^2}} \right]$$

Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

A force $$\overrightarrow F = (40\widehat i + 10\widehat j)N$$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\overrightarrow r $$ at time t = 10 s, will be :