Since, the particle is moving with constant acceleration. Acceleration = Constant, (the acceleration-time graph is parallel to the time axis, and acceleration is positive) a=‌
dv
dt
As we know, ‌
dv
dt
=C⇒∫dv=C‌∫dt ⇒‌‌v=Ct+C0 The velocity-time graph is straight line with positive slope V=‌
dx
dt
As we know, ‌
dx
dt
=Ct+C0
⇒‌‌∫dx=∫(Ct+C0)dt⇒x=‌
Ct2
2
+C0t+C1
This equation shows that the distance-time graph is upward concave parabola.