From the given velocity-displacement graph, for 0≤x≤200, the graph is a straight line i.e., varying linearly. As, the equation of straight line is y=mx+c Here, it can be given as v=mx+c where, m= slope =
(50−10)
200−0
=
1
5
and c=10 ⇒v=
x
5
+10 As, acceleration, a=
dv
dt
=
vdv
dx
a=(
x
5
+10)
d
dx
(
x
5
+10) [using Eq. (i)] =(
x
5
+10)(
1
5
)=2+
x
25
For x=0,a=2+
0
25
=2ms−2 and for x=200,a=2+
200
25
=10ms−2 Therefore, the graph will have straight line till x=200 and for x>200;v= constant and a=0 So, from the graphs given in the options, the above conditions are satisfied in option (a) only.