A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms^$$-$$1 to 20 ms^$$-$$1 while passing through a distance 135 m in t second. The value of t is

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

A car moves from X to Y with a uniform speed v_u and returns to Y with a uniform speed v_d. The average speed for this round trip 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 ?