Motion in A Str...

A particle travels so that its acceleration is given by $$\vec{a}=5\,cos\,t\hat {i}-3\,sin\,t\hat {j}$$. If the particle is located at $$(-3,2)$$ at time $$t=0$$ and is moving with a velocity given by $$(-3\hat {i}+2\hat {j})$$. Find
(i) the velocity $$\begin{bmatrix}\vec{v}=\int \vec{a}.dt\end{bmatrix}\:time\:t$$
(ii) the position vector $$[\vec{r}=\int \vec{v}.dt]$$ of the particle at time $$(t>0)$$.

Two balls were thrown vertically upwards with different velocities, what is the shape of the graph between distance between the balls and time before either of the two collide with ground?

A thief is running away on a straight road with a speed of $$9  \ ms^{-1}$$. A police man chases him on a jeep moving at a speed of $$10 \  ms^{-1}$$ If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take. for the police man to catch the thief?

A stone is thrown upwards from a tower with a velocity $$50\, ms^{-1}$$. Another stone is simultaneously thrown downwards from the same location with a velocity $$50\,ms^{-1}$$ . When the first stone is at the highest point, the relative velocity of the second stone with respect to the first stone is (assume that second stone has not yet, reached the ground  

A ballon starts rising from the ground with an acceleration of $$1.25 \ m/s^{2}$$. After $$8\ s$$ a stone is released from the balloon. The stone will (take $$g=10\ m/s^{2}$$)

Which of the following is not an example of acceleration?

Consider a train which can accelerate with an acceleration of $$20 {cm}/{{s}^{2}}$$ and slow down with deceleration of $$100 {cm}/{{s}^{2}}$$. Find the minimum time for the train to travel between the stations $$2.7 km$$ apart.

An aeroplane flies along a straight line from A to B with air speed $$V$$ and back again with the same air speed.If the distance between A and B is $$l$$ and a steady wind blows perpendicular to AB with speed $$u$$, the total time taken for the round trip is

A person drops a metallic sphere from the top of a tower of height 125 m. Another person at a distance of 80 m from the foot of the tower hears the sound of the sphere hitting the ground after a time interval of 5.25 s. Find the velocity of the sound in air.($$g = 10  {ms}^{-2}$$)

At a certain acceleration, a racing car takes $$5 s$$ to double its speed while moving at $$2 m{s}^{-1}$$. If now, it moves at $$4 m{s}^{-1}$$, at the same acceleration, what time will it take to double its speed?