A truck has to carry a load in the shortest time from one point to another at a distance L from the first. It can only start up or slow down at the same accelertion a. What maximum velocity must the truck attain to satisfy this condition ?

A stone of mass m is tied to an elastic string of negligble mass and spring constant k. The unstretched length of the string is L and has negligible mass. The other end of the string is fixed to a nail at a point p. Initially the stone is at the same level as the point P. The stone is dropped vertically from point P. (a) Find the distance y from the top when the mass comes to rest for an instant, for the first time. (b) What is the maximum velocity attained by the stone in this drop? (c) What shall be the nature of the motion after the stone has reached its lowest point?

From point A located on a highway (figure) one has to get by car as soon as possible to point B located in the field at a distance l from the highway. It is known that the car moves in the field eta times slower than on the highway. At what distance from point D one must turn off the highway?

A particle of mass m carrying charge q is projected with velocity v from point P toward aninfinite line of charge from a distance a . Its speed reduces to zero momentarily at point Q , which is at a distance a//2 from the line of charge. If another particle with mass m and charge -q is projected with the same velosity v from P toward the line of charge, what will be its speed at Q ?

Two buses start from the opposite points of a main road, 150 km apart. The first bus runs for 25 km and takes a right turn and then runs for 15 km. It then turns left and runs for another 25 km and takes the direction back to reach the main road. In the meantime, due to a minor break down, the other bus has run only 35 km along the main road. What would be the distance between the two buses at this point ?

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.2 m//s^2 and the automobile has an acceleration of 3.5 m//s^2 . The automobile overtakes the truck when it (truck) has moved 60 m. (a) How much time does it take the automobile to overtake the truck ? (b) How far was the automobile behind the truck initially ? (c) What is the speed of each during overtaking ?