A particle moves in a straight line with an a–t curve shown in figure. The initial displacement and velocity are zero .
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(a, b, c, d)
Area under a-t curve :
Δ v = Area 1 = 2 × 4 = 8
v – u = 8
v = u + 8 = 0 + 8 = 8 m/s
v ′ – v = Area 2 = 
= – 8 m/s
v ′ = v – 8 = 8 – 8 = 0
final velocity is zero at t = 10 sec
Displacement: Can be directly calculated from a–t cure without using v–t curve.
Δ S = u 0 t 0 + (area under a–t curve) (t 0 – t c )
Where Δ S = displacement
u 0 = initial velocity
t 0 = total time
t c = Abscissa of centroid of corresponding area
Centroid of area 1: C 1 = (1,2)
Centroid of area 2 : C 2 = 
Δ S = 0 + 8 [10 – 1] + 
= 8 × 9 + 
= 8 
= 8 × 
= 8 × 3.666
= 8 × 3.67
Δ S = 29.36 m
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