A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate $${f \over 2}$$ to come to rest. If the total distance traversed is 15 S, then

A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is

The relation between time t and distance x is t = ax² + bx where a and b are constants. The acceleration is

A bullet fired into a fixed target loses half of its velocity after penetrating $$3$$ $$cm.$$ How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?