Question

Find the total displacement made by the object in 7 sec from origin where he has initial velocity of 10m/s according to the graph given below?

(a) 30m
(c) 60m
(b) 40m
(d) 20m​

Answer 1

Explanation:

displacement=

area of rectangle OABE+ area of trapezium ABCD

=b×h+1/2(sum of ll side)×h

=3×10 + 1/2(10+5)×4

=30+30

=60m

Answer 2

Answer:

The total displacement made by the object is 60m.

Explanation:

Given the $v~-~t$ graph.

Total time for the displacement,  $t=7 ~s$

Initial velocity of the object,  $u= 10m/s$

Displacement of the object is given by the area under the  $v~-~t$ graph.

Therefore, the displacement from the graph

= area of rectangle OABE + area of trapezium ABCD

$= b\times h+\frac{1}{2} (a+b)\times d$

where b and h are the breadth and height of the rectangle respectively, a and b are the lengths of parallel sides of trapezium and d is the distance between the parallel sides.

substituting the values from the graph,

$=3\times 10 + \frac{1}{2} (10+5)\times 4$

$=30 + 15\times 2$

$=30+30$

$=60m$

Therefore, the total displacement made by the object is 60m.