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

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

Step-by-step explanation:

For uniform acceleration we know that

`(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

`(dx)/(dt) = v_o + at`

again by integration both sides

`x - x_0 = v_o t + (1)/(2)at^2`

`x = x_0 + v_0t + (1)/(2)at^2`

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