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 ?

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is

A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise?
(Take g = 10 m/s².)

The displacement x of a particle varies with time t as x = ae^$$-$$at + be^{$$\beta $$t}, where a, b, $$\alpha $$ and $$\beta $$ are positive constants. The velocity of the particle will