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 ?

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

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.)

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time ? (Given g = 9.8 m/s²)