Question

If I'm given 6 position vs time graphs and I need to put their average velocities and average speeds in order from greatest to least. What is the difference between the two and how do I calculate them? Please help my test is tomorrow.

Answer 1

The graphs with the largest positive slope will have the largest velocity, The graphs with the largest slope (positive or negative) will have the largest speed.

Explanation:

The slope (derivative `{dx}/{dt}`, or rise over run) of a position vs. time graph gives you the velocity.

Average velocity = `{x_2 - x_1}/{t_2 - t_1}`
where `x_2` is the ending position and `x_1` is the starting position, and `t_2` is the ending time and `t_1` is the starting time.

If you ever get confused, it can be useful to think of units. Velocity is given in something like meters per second, so the number of meters you travel divided by the time you travel gives you the average velocity.

The graph with the largest positive slope (steepest line) will have the greatest velocity , followed by graphs with small positive slopes, then small negative slopes, then large negative slopes.

You can either try to eyeball how step the line is or pick two points and plug it into the equation above.

Velocity is a vector quality, it includes both a magnitude (number) and a direction (sign):
- 5 m/s, + 10 m/s

Speed is a scalar quantity, it includes just a magnitude (number):
5 m/s, 10 m/s
You can consider it the absolute value of the velocity (sign is not important).

So the graph with the largest slope (positive or negative) will have the largest speed , then graphs with small slopes (positive or negative).