Motion in A Str...

A stone projected up vertically with a velocity v, reaches points x, y and z in its path with velocities $$\displaystyle \frac { v }{ \sqrt { 5 }  } ,\frac { v }{ \sqrt { 10 }  } and\frac { v }{ \sqrt { 15 }  } $$ respectively. Find the ratio xy : yz.

A bike moving along a straight road covers $$35$$ m in the $$4$$th second and $$40$$ m in the $$5$$th second. What is its initial velocity and acceleration (if the acceleration is assumed to be uniform )? 

Find the initial velocity of projection of a ball thrown vertically up if the distance moved by it in 3rd second is twice the distance covered by it in 5th second.$$\displaystyle (Take g = 10\ { ms }^{ 2 })$$

An object travels 10 s with uniform acceleration along a straight line path. During this period if the velocity of the object is increased from $$\displaystyle { \ 5\ ms }^{ -1 } to { \ 25\ s }^{ -1 }$$, then find the distance travelled by the body?

A stone is dropped by a person from the top of a tower, which is 200 m tall. At the same time another stone is thrown upwards, with a velocity of $$\displaystyle 50\ { ms }^{ -1 }$$  by a person standing at the foot of the tower. Find the time after which two stones meet.

Two cars arrive at certain point with velocity of $$\displaystyle { 30\ ms }^{ -1 } , { 25\ ms }^{ -1 } $$ and travel in a straight line with uniform acceleration $$\displaystyle { 0.25\ ms }^{ -2 }\ and\  { 0.5\ ms }^{ -2 } $$ respectively.
(A) Find the distance at which they meet again.
(B) Also determine the time after which the final velocity one of the cars is equal to the initial velocity of the other.

When a body is dropped from a tower, it covers 75% of total height of the tower in the last second of its fall. What is the total height of the tower? 

A freely falling body crosses points P, Q and R with velocity V, $$2$$V and $$3$$V respectively. Find the ratio of the distance PQ to QR.

A car moves with a constant velocity of $$\displaystyle { 10\ ms }^{ -1 }$$ for 10 s along a straight road. Then it moves with uniform acceleration of $$\displaystyle { 2\ ms }^{ -2 }$$ for $$5$$ seconds. Find the total displacement at the end of the 15 s of its motion. 

A body is dropped from a height of $$2$$ m. It penetrates into the sand on the ground through a distance of $$10$$ cm before coming to rest. What is the retardation of the body in sand?