The velocity-time graph of a moving body is given below in figure Find — (i) The acceleration in parts AB, BC and CD. (ii) Displacement in each part AB, BC, CD, and (iii) Total displacement.

Let E be the point at t = 4 and F be the point at t = 8 as labelled in the graph below:

(i) Acceleration in part AB = slope of AB

Slope of AB = 30-0\over 4-0

= 30\over 4

= 7.5 ms^-2

Hence, Acceleration in part AB = 7.5 m s^-2

Acceleration in part BC = slope of BC

We observe from the graph that there is no change in velocity in part BC. Hence, Acceleration in part BC = 0 m s^-1

Acceleration in part CD = slope of CD

= 0-30\over 10-8

= -30\over 2

= -15 ms^-2

Hence, Acceleration in part CD = -15 m s^-1

(ii) Displacement in each part is as follows —

(a) Displacement of part AB = Area of triangle ABE

= 1/2 × base × height

= 1/2 × 4 × 30 =60 m

Hence, Displacement of part AB = 60 m

(b) Displacement of part BC = Area of Square EBCF

= length × breadth

Substituting the values in the formula above, we get,

= (8 – 4) × (30 – 0)

= 4 × 30 = 120

Displacement of part BC = 120 m

(c) Displacement of part CD = Area of triangle CDF

= 1/2 × base × height

= 1/2 × 2 × 30 = 30 m

Hence, Displacement of part CD = 30 m

(iii) Total displacement = 60 + 30 + 120 = 210