AIEEE 2008 Solved Paper

For the body starting from rest
x1=0+‌

1

2

at2⇒x1=‌

1

2

at2
For the body moving with constant speed
‌x2=vt
‌∴x1−x2=‌

1

2

at2−vt
‌‌‌⇒‌

d(x1−x2)

dt

=at−v
at t=0,‌‌x1−x2=0, so graph should start from origin.
For at<v; the slope is negative that means x1−x2<0 so initially velocity of 1 st body is less than second body and velocity of 1 st body is increasing gradually.
For at=v; the slope is zero. So x1−x2=0 it means here velocity of both the bodies are same.
For at>v; the slope is positive. So x1−x2>0 it means here velocity of first body is greater than second body.
We know the relation between distance and time is.
S=ut+‌

1

2

at2, which is a equation parabola. So the graph should be a parabola.
These characteristics are represented by graph (b).