Can velocity-time graphs ever have curved lines?

Question

If so, what does the curved line mean? I know in distance time graph you can, and that means that the object is accelerating.

A question in my book asks me to "plot the data on a velocity-time graph. Connect the points with a smooth curve".

I'm confused because in class, the teacher has never mentioned curved lines in v-t graphs.

Answer 1

Actually if the velocity-time is a curved line, it also means the object is accelerating. However, if the velocity versus time is a constant velocity value, then the object is not accelerating at all. If the velocity-time plot is a linear plot, then the acceleration is constant. If the velocity-time plot is curved, the object is accelerating, though the amount of acceleration is also changing with time. Each of these relates to the next.

Answer 2

Velocity Time Graph

Answer 3

A curved line on a velocity-time graph means that the accleration is not constant, and not necessarily that there is positive accleration. If you have ever been a car starting from a stop and getting up to speed on an Interstate, and plotted the velocity vs time, you would notice that it is a curved line

Answer 4

absolutely. They can curve if the acceleration is changing. Any kind of jerky motion will cause changes in acceleration and therefore curves in the v vs t graph. In fact, we sometimes call the time derivative of acceleration "jerk".

An example of unchanging acceleration is freefall. The acceleration is always g.

Now imagine something like simple harmonic motion. The direction of motion and the velocity and the force and the higher derivatives are constantly changing.