Accelerated motion could be changing speed, or changing direction, or both.
If it's only the direction changing and not the speed, then you'll never see it on a distance/time graph.
If the speed is changing, then a velocity/time graph can be any kind of a line except horizontal or vertical, and a distance/time graph must be curved.
Answer:
Accelerated motion is represented by a CURVED line on a nonlinear distance-time graph.
Explanation:
For uniform acceleration we know that
[tex]\frac{dv}{dt} = a[/tex]
now integrating both sides we will have
[tex]\int dv = \int adt[/tex]
now after integration we will have
[tex]v - v_o = at[/tex]
now we have
[tex]v = v_o + at[/tex]
again we know that
[tex]\frac{dx}{dt} = v_o + at[/tex]
again by integration both sides
[tex]x - x_0 = v_o t + \frac{1}{2}at^2[/tex]
[tex]x = x_0 + v_0t + \frac{1}{2}at^2[/tex]
now since this equation is a quadratic equation so here distance time graph must be a curved graph
