1) A boat which has speed of 5 km / h in still water across a river of width of 1km along the shortest path in 15 minutes . The velocity of river in km / s is : -

1 ) A boat which has speed of 5 km / h in still water across a river of width of 1km along the shortest path in 15 minutes . The velocity of river in km / s  is : -

A ) 3  km / h   ,                                 B ) 7  km / h   ,

C ) 18  km / h   ,                              D ) 21 km / h  ,

Correct Answer : -   A ) 3  km / h   ,

Solution : -

Let the velocity of river be  ‘x’  km / hr .

Speed of boat  =  5 km / h  ,  And

Width of river ( AB )  =  1 km / hr .

Time taken to cross the river by boat  =  15 minutes .

So distance covered by boat  : -  d  =  v t  ,

d  =  5 x 15 / 60  =  1.25  km / hr .

Now  ,  AB = 1 km / hr    ,  And   AC = 1.25 km / hr .

And  angle  β = 90°  .

So , 

( AB ) ^ 2  +  ( BC ) ^ 2  =  ( AC ) ^ 2  ,

1  +  ( BC ) ^ 2  =  ( 1.25 ) ^ 2  ,

So ,    BC  =  0.75  km .

So  ,  distance covered by river water in 15 minutes is  0.75 km / hr .

Velocity of river : -  v  =  d / t  =  0.75 / (1/4)  ,

v = 3  km / h   ,   Answer .

 

2 ) The velocity time graph of a car is moving along a straight road is shown in figure .  The average velocity of car in first 25 seconds is : -

Choose single option from these following : -

A ) 5 m / s ,                                                          B ) 10 m / s ,      

C ) 14 m / s ,                                             D ) None of these ,

Correct Answer : -   C ) 14 m / s ,

Solution : -

3 ) The velocity – time graph for particle is moving in a straight line . The sum of two shaved areas represents : -

A ) increase in displacement of a particle ,

B ) the average velocity of a particle ,

C ) average acceleration of particle ,

D ) the distance moved by a particle ,

Correct Answer : -  D ) the distance moved by a particle ,

Solution : -