Motion in A Str...

A particle starts from rest travels a distance $$x$$ with uniform acceleration, then it travels a distance $$2x$$ with uniform speed, finally, it travels a distance $$3x$$ with uniform retardation and comes to rest. If the whole motion of the particle is a straight line, then the ratio of its average velocity to maximum velocity is

A ball is thrown vertically upwards with a velocity of $$10 \, ms^{-1}$$. It returns to the ground with a velocity of $$9 ms^{-1}$$ .If $$g=9.8 ms^{-2}$$, then the maximum height attained by the ball is nearly (assume air resistance to be uniform)

A stone is allowed to fall from top of a building and covers half of the height in last second of its motion. The time taken by stone to reach the bottom of building is?

A train starts from station $$A$$ with uniform acceleration $$\alpha$$ for some distance and then goes with uniform retardation $$\beta$$ for some more distance to come to rest at station $$B$$. The distance between station $$A$$ and $$B$$ is $$4\ km$$ and the train takes $$4$$ minutes to complete this journey. If $$\alpha$$ and $$\beta$$ are in km $$(min)^{-2}$$ then $$\dfrac {1}{\alpha} + \dfrac {1}{\beta} =$$.

A man $$m=80kg$$ is standing on a trolley of mass $$320kg$$ on a smooth surface. If man starts walking on trolley along rails at a speed of $$1m{s}^{-1}$$, then after $$4$$ sec, his displacement relative to ground is

A person sees a stone fall from the top of a distant building and notes that it takes 1.5 s for the stone to fall the last third of the way to the ground. With ignoring air resistance, the height of the cliff in meters is 

A car starts from rest and moves on straight line with constant acceleration $$a_{0}$$. After time $$t_{0}$$, brakes is applied which cause of deceleration of magnitude as initial acceleration. The distance travelled by car is

A particle starts from rest and traverses a distance $$l$$ with uniform acceleration, then moves uniformly over a further distance $$3\ l$$ under uniform retardation. Assuming entire motion to be rectilinear motion the ratio of average speed over the journey to the maximum speed on its way is

Two bodies were thrown simultaneously from the same point at time $$t=0$$, one straight up and other at an angle $${30^ \circ }$$ with horizontal. the initial speed of the each body is equal to $$30m/s$$. The magnitude of relative displacement between the two bodies at $$t=2s$$ will be $$(g = 10m/{s^2})$$  

From a motorboat moving downstream with a velocity $$2\ m/s$$ with respect to river, a stone is thrown. The stone falls on an ordinary boat at the instant when the motorboat collides with the ordinary boat. The velocity of the ordinary boat with respect to the river is equal to zero. The river flow velocity is given to be $$1\ m/s$$. The initial velocity vector of the stone with respect to earth is