Motion in A Str...

Two particles $$A$$ and $$B$$ are initially located on $$y-axis$$ with distance $$l$$ apart. They start moving at time $$t = 0$$ such that the velocity $$\vec u$$ of $$B$$ is always along the $$x-axis$$ and velocity $$\vec v$$ of $$A$$ is continuously aimed at $$B.$$ At $$t = 0, \vec { u }$$ is perpendicular to $$\vec { v }.$$ The particles will meet after time

A balloon is moving up from the ground in such a way that its acceleration is linearly decreasing with its  height above the ground. It starts from the ground with acceleration $$4 \mathrm { m } / \mathrm { s } ^ { 2 }$$  and with zero initial velocity Its acceleration becomes zero at a height $$3\mathrm { m } .$$ The speed of the balloon at a height $$1.5\mathrm { m }$$  is:

An automobile and a truck start from rest at the same instant, the automobile initially at some distance behind the truck. The truck has a constant acceleration of $$2.2m/s^{2}$$ and the automobile has an acceleration of $$3.5m/s^{2}$$. The automobile overtakes the truck when it (truck) has moved $$60m$$. How much time does it take the automobile to overtake the truck and how far behind the automobile the truck initially was ?

Two particles start moving from the same point along the same straight line .the first constant veiocity v and the second with constant accleration a. During the time that the second catch the first the greatres distance between the particles is 

Two bodies of different masses are dropped simultaneously from same height,If air friction acting them is directly proportional to the square of their mass then  

A body is moving with a uniform acceleration covers 200 m in the first 2s and 220 m in the next 4s. find the velocity in $${ms}^{-1}$$ after 7s. 

The motion of a particle is described by the law $$a = t ^ { 3 } - 3 t ^ { 2 } + 5$$ where $$a$$ is the acceleration is $$\mathrm { m } / \mathrm { s } ^ { 2 }$$ and $$t$$ is time in second. The position and velocity of the particle at $$t = 1s$$ are $$8.30m$$ and $$6.25 m/s$$. Calculate the position at $$t = 2s$$. 

A body falling freely from rest covers $$\dfrac { 7 }{ 16 } $$ of the total height in the last second of its fall. The height from which it falls is

A trolley of mass 300 kg carrying sand 200 kg (in it) is moving uniformly with speed of 40km/h on a frictionless track. After a while sand starts leaking out of a hole on the track. What is the speed of the trolley after entire sand is leaked out?

A boat takes 2 hours to travel 8 km and back in still water. If the velocity of the water is 4 km/h then the time taken for going upstream of 8 km and then coming back would be