Motion in A Str...

A sprinter has to cover a total run of $$100 m$$. She increases her speed from rest under an uniform acceleration of $$1.0 m/s^{2}$$ up to three quarters of the total run and covers the last quarters with uniform speed. The time she takes to cover the first half, and to cover the second half of the run will be 

A man throws ball 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 ?

An object is thrown vertically upward and experiences an air resistance opposing its motion with magnitude proportional to its speed. Which of the following graphs best represents the variation of the acceleration, a, of the object with time t, starting from the moment when the object leaves one's hand up to the time when it returns to the ground? (Take downward as positive)

The speed $$v$$ of a particle moving along a straight line, when it is at distance $$( \mathrm { x } )$$ from a fixed point of the line is given by $$v ^ { 2 } = 108 - 9 x ^ { 2 } .$$ (all quantities are in cgs units) 

A student is standing at $$50 \ m$$ from a bus, and at the same time when bus starts with a constant acceleration of $$ 1 \ m /{s  }^{ 2 } $$, student runs behind it to catch it, at a uniform speed $$u.$$ Find minimum value of $$u$$ so that student can catch the bus:

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

A car accelerates from rest at a constant rate $$\alpha$$ for some time after which it decelerates at a constant rate $$\beta$$ to come to rest. If the total then, the time elapsed it $$t$$, the distance travelled by the car is

A man  weighing $$80 kg$$ and a lady weighing $$40 kg$$ standing on a lift. The lift moves downwards with uniform acceleration of $$7.35m/{ s }^{ 2 }$$. The factors by which their weights are reduced apparently will be in the ratio of 

If a smooth stright tunnel is cut at any orientation through earth, then a ball released from one end will reach the other end in time (neglect earth rotation)

After some time the bus will be left behind. If the bus continues moving with the same acceleration, after what time from the beginning, the bus will overtake the cyclist?