The velocity - time graph of a body is as shown , So find the displacement of a body in 6 seconds ?

1 )  The velocity - time graph of a body is as shown , So find the displacement of a body in 6 seconds ?

A ) 3 ,                                               B ) 6 ,

C ) 12 ,                                            D ) None of these ,

Correct Answer : -  B ) 6 ,

Solution : -

So we have divided the whole diagram in 4 parts or figures .

So figure # 01 : -

It is like a rectangle and we simply calculate displacement by area formula : -

For example ,  area of rectangle = L x W = 2 x 2 = 4 .

So , figure # 02 : -

It is like a trapezium and we have formula : -

Area of trapezium  =  ( 1 /2 )  x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides = ( 1 / 2 ) x ( 2 + 4 ) x 1 = 3 .

So , figure # 03 : -

It is like a triangle and we have formula : -

Area of triangle  =  ( 1 / 2 ) x L  x W =  ( 1 / 2 ) x 4 x 1  =  2 .

So , figure # 04 : -

It is like a triangle and we have formula : -

Area of triangle  =  ( 1 / 2 ) x L  x W =  ( 1 / 2 ) x ( -3 ) x 2  =  -3 .

It has negative sign because displacement is in downward direction .

So , now we add all the area of this diagram : -

Total displacement =  ( figure # 01 ) +  ( figure # 02 ) + ( figure # 03 ) + ( figure # 04 ) ,

Total displacement =   4 + 3 + 2 + ( -3 )  =  6  ,   Answer .

 

2 )  The velocity - time graph of a body is as shown , So find the displacement of a body in 5 seconds ?

A ) 1  ,                                              B ) 3  ,  

C ) 5  ,                                             D ) None of these ,

Correct Answer : -  A ) 1  , 

Solution : -

So we have divided the whole diagram in 4 parts or figures .

So figure # 01 : -

It is like a triangle and we simply calculate displacement by area formula : -

For example ,  area of triangle = ( 1 / 2 ) x L x W = ( 1 / 2 ) x 1 x 1 =  1 / 2 .

So , figure # 02 : -

It is like a square and we have formula : -

Area of square  =  L x W  =  1 x 1 = 1 .

So , figure # 03 : -

It is like a triangle and we have formula : -

Area of triangle  =  ( 1 / 2 ) x L  x W =  ( 1 / 2 ) x 1 x 1  =  1 / 2 .

So , figure # 04 : -

It is like a triangle and we have formula : -

Area of triangle  =  ( 1 / 2 ) x L  x W =  ( 1 / 2 ) x ( -1 ) x 2  =  -1  .

So , now we add all the area of this diagram : -

Total displacement =  ( figure # 01 ) +  ( figure # 02 ) + ( figure # 03 ) + ( figure # 04 ) ,

Total displacement =  ( 1 / 2 ) + 1 + ( 1 / 2 ) - 1   =  1  ,   Answer .

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