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 .
Now go to online quiz section and Physics Quiz 11 is uploaded related to these mcqs , so check your preparation by this link : -
