Area ABCD = Area of Rectangle ABED + Area of DEC

= AB ´ AD + 1 DE ´ EC
                      2

= (3 - 1) ´ (30 - 0) + 1 (3 - 1) ´ (70 - 30)
                                  2

= 60 + 40

= 100 m.

Now, displacement between 1st to 3rd sec is
= 10 ´ 3 + 1 ´ 10 ´ 32 - {10 ´ 1 + 1 ´ 20 ´ 12 }
                  2                                    2
= 10 [3 + 9] - { 10 (1 + 1) }

= 10 {12 - 2}

= 10 { 10}

= 100 m

Thus displacement in a given interval is
= Area under velocity-time graph for the given interval.

This result is obvious, as can be seen from

v = ds (in scalar form)
      dt

\ ds = v dt

Index

2.1 Definitions
2.2 Motion in one Dimension
2.3 Motion in two Dimension

Chapter 3