Question

How would zero velocity and nonzero acceleration be represented on a velocity-time graph?

My physics teacher did mention that with zero velocity and non-zero acceleration, the resulting motion would be "speeding up". I don't quite understand this comment as well as how to graph such motion on a velocity-time graph.
Thanks!

Answer 1

Zero velocity and nonzero acceleration are two different cases.

Explanation:

1. An object having zero velocity implies that it is stationary at a particular location. If we plot it on a velocity-time graph which represents velocity on the `y`-axis and time on the `x`-axis, it is represented by `x`-axis
   Value of `y` (velocity), is `0` for all values of `x` (time).
   graph{y=0x [-2, 27.49, -2, 9.49]}
   Represented by blue line in the figure above.
2. Nonzero acceleration, assuming it is constant. It could be either positive or negative. The general kinematic equation representing such a motion is

   `v=u+at`
   `v` is final velocity after time `t`, `a` is the acceleration and `u` is the initial velocity.

Compare it with the equation of a straight line in the slope-intercept form

`y=mx+c`
We see that slope of the line represents acceleration.

As shown in the figure above, positive slope represents acceleration, (speeding up) from `t=0` to `t=15s`.
Slope is negative from `t=15` to `t=25s`. This represents deceleration or retardation (slowing down).