A particle moving along x-axis has acceleration f, at time t, given by f = f₀$$\left( {1 - {t \over T}} \right),$$ where f₀ and T are constants.The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle's velocity (v_x) is

The positions x of a particle with respect to time t along x-axis is given by x = 9t² $$-$$ t³ where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t $$-$$ t³. How long would the particle travel before coming to rest ?