Question-21 The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance travelled by the body in time 0\ to\ 8\ s is
(A) 8:5
(B) 3:5
(C) 5:9
(D) 7:4
Answer : (C)
Explanation:
Area under the curve of velocity – time graph gives the distance travelled by the particle.
If the area under the curve is above the x – axis, then the displacement of the particle is positive and if the area under the curve is below the x – axis then the displacement of the particle is negative.
∴ Displacement of the particle will be given by
Displacement = A_1-A_2+A_3-A_4+A_5=(3\times2)-(1\times2)+(2\times2)-(1\times2)+(2\times2)
= 6 − 2 + 4 − 2 + 4 = 10
Distance travelled will be magnitude of the area under the curves.
∴ Distance = A_1+A_2+A_3+A_4+A_5=(3\times2)+(1\times2)+(2\times2)+(1\times2)+(2\times2)
= 6 + 2 + 4 + 2 + 4 = 18
\frac{Displacement}{Distance}=\frac{10}{18}=\frac{5}{9}