Velocity

[1] Velocity is a measurement of speed with a direction of motion, a vector quantity so it has both magnitude and direction are needed to define it (velocity vector).

Quiz

Average velocity

An object in motion's average velocity is its total displacement/position change, divided by the total time taken for the motion. 

• displacement: measure of speed and direction

Not to be confused with average speed. 

Average speed shows an object's speed no matter its direction, while average velocity shows both speed and direction, a more complete motion description.

In short, direction doesn't matter in speed but does in displacement.

Velocity describes position change overtime. 

For instance, a bike travelling east at a constant speed of 11 m/s has a velocity of 11 m/s [E]. Since it has direction and magnitude, average velocity is a vector quantity. 

                                                                                                             →

The SI unit for velocity is metre per second (m/s). Its symbol is vav.

Steeper the graph, greater the object's displacement in a given time interval and higher its velocity, which can be confirmed using the info in Figure 2.

Like in math, Δd, the graph's slope formula is either 

                                         →     →

                                         Δd2 - d1                        →

slope = rise/run, or m = ________ , or m = Δd / Δt

                                            t2 - t1

The equation gives a moving object's average velocity: 

            →

 →       Δd

 vav  =  ___

    Δt

The rolling ball's velocity is 4 m/s [E]. Note that the graphs' slope in Figure 2 and 3 are the same, 4 m/s [E]. The 2 motions are different in that the motion in Figure 2 started 0 m away from the observer, whereas the motion in Figure 3 has an initial position of 10 m [E] from the observer. Calculating average velocity from the slope of a position-time graph is a very useful method as it's often hard to measure directly. But position can be easily done with equipment like tape measures, motion sensors, and laser speed devices.

Velocity (a vector quantity) is to speed (a scalar quantity) as displacement (a vector quantity) is to distance (a scalar quantity). The average velocity equation should thus be similar to the one for average speed, but velocity and displacement are vectors:

Average velocity Example 1

Calculate the average velocity of the balloon: A balloon's position changes as the windy blows it 82 m [N] away from a child in 15s. 

Solution:

Substitute the displacement (82 m) and time (15 s.) into the average velocity equation:
            →

  →       Δd

• vav = ___

    Δt

              →

   →      82

• vav = ___

            15

• vav = 5.5 m/s [N] is the average the ballon's velocity.

Average velocity Example 2

A train travels at 22.3 km/h average velocity [W]. 

How long (Δt) will it go in a displacement of 241 m [W]?

Solution:

Substitute the average velocity (22.3 km/h) and the displacement (241m.) into the average velocity equation to calculate the time (Δt) it will take for the train to go 241 m: 

            241    

22.3 = ____ 

             Δt

Since the measurement units aren't the same, displacement is converted from kilometers/hours to meters/seconds by either being...

1. multiplied by ratios of 1 

                     22.3 km x 1000 = 22300 m           22300 m.     

Method 1: _____________________________  =  __________

                        h x 60 x 60                     3600 s

or...

2. by directly multiplying the scale of the required units (1 km = 100 m and 1 h = 3600 s).

Method 2:    22.3 km       1 h.           1 m.         1000 m        22300 m.

                     ________ x ______ x  _______ x _________ = _________

                    h              60 m.        60 s.          1 km            3600 s

                     241 m

22300 m/h = _______ = 0.01081 meter per hours/38.91600 meter per seconds

Δt

Uniform and non-uniform velocity motion

Motion with uniform/constant velocity is motion in a straight line. 

It's an object's basic motion type, except for being at rest. 

Note that both requirements (constant speed and straight line) must be met for its velocity to be uniform. 

In contrast, motion with non-uniform velocity is when an object's speed or direction isn't constant, indicating; either speeding up, slowing down, changing direction, or combined.