Question

Accelerated motion is represented by a _____ line on a nonlinear distance-time graph.

Answer 1

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 2

Answer:

Accelerated motion is represented by a CURVED line on a nonlinear distance-time graph.

Explanation:

For uniform acceleration we know that

$\frac{dv}{dt} = a$

now integrating both sides we will have

$\int dv = \int adt$

now after integration we will have

$v - v_o = at$

now we have

$v = v_o + at$

again we know that

$\frac{dx}{dt} = v_o + at$

again by integration both sides

$x - x_0 = v_o t + \frac{1}{2}at^2$

$x = x_0 + v_0t + \frac{1}{2}at^2$

now since this equation is a quadratic equation so here distance time graph must be a curved graph