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Main Kinematics & Dynamics Speed & Velocity Lesson I.4.2 Unit I:Kinematics & Dynamics

Velocity - Lesson I.4.2

Key Terms:

Instantaneous velocity | Constant velocity | Average velocity | IL, NUM, CCT

Velocity (average velocity) is an objects' displacement (change in position) per unit time. Since velocity is derived from a vector quantity, displacement, it is also a vector quantity and therefore requires a direction as well as a magnitude. The SI unit for velocity is m/s.

We can also use one of our methods of vector resolution to determine the displacement for non-collinear vectors and then use our average velocity equation as in our check point.

For example:
A plane is flying at for 20 minutes and travels a distance of 120 km [E]. The pilot then changes its direction to [N 45 E] and travels 70 km in 13 minutes. What is the average velocity of the plane?

Since average velocity is determined by displacement and the change in time, in this problem you must first determine the displacement of the plane using vector resolution (vectors are non-collinear).

We will use the vector component method to determine the displacement.

  • Step 1: Write down the given information and determine the angle for each vector F.

  • Step 2: Break each vector down into its x and y components.

    Eq1_4_2b

  • Step 3: Add the collinear vectors algebraically.

    Eq1_4-2c
    Eq1_4_2d

  • Step 4: Use the Pythagorean theorem to determine the magnitude of the resultant vector.

    Eq1_4_2e

  • Step 5: Use a trigonometric ratio to determine the angle from the positive x-axis to the resultant vector.

    Eq1_4_2f

  • Step 6: Convert this angle into north-south directions.

    Since R is measured counterclockwise from the positive x-axis, the angle from north to east would be 90 -16 = 74 . The resultant vector, displacement, would therefore be 181 km [N 74 E].

Now that we know displacement, we can convert our time to hours and then use the average velocity equation to answer our original question.

Eq1_4_2g
Eq1_4_2h

We have just discussed average velocity; however, it is also important to understand instantaneous and constant velocity.

Instantaneous velocity is the instantaneous speed in a specific direction.

Constant velocity occurs when the object has the same displacement in equal periods of time. It is an example of uniform motion.

Average velocity can be equal in magnitude to average speed if the object moves in a straight line (i.e. when the displacement is equal to the distance traveled). If the object travels along a curved path then the average velocity will be less than the average speed since displacement will be less than the distance traveled.

  
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