Velocity
Adding at an angle :: | :: Position - Time Graphs

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Velocity is the speed along a direction. Like displacement, it is also a vector quantity. Velocity can be communicated in a variety of way including a symbol,; an actual quantity, 40 km/h [E], or a labelled arrow such as ones used in displacement.

These ways of communication mentioned above are used to represent constant velocity, which means both the size and direction stay the same.

To calculate velocity you must use the change in displacement along with the change in time:

Average Velocity

Average velocity is the overall change in positions from start to finish. We need to calculate average velocity for two reasons.

1. If we know the resultant displacement and time but have no information on the velocities at any time during the trip; or
2. If the velocity varies (either in direction or magnitude) during the journey, but we are only interested in the average velocity of the entire trip.

The main equation for calculating velocity is:

Sample for Velocity (not average velocity)

A plane travels at a constant speed across the Atlantic ocean from Asia to North America. It has a displacement of 100 km in a time of 3.9 hours. What was the planes velocity?

Step 1: State the given information

= 100 km [E]
t = 3.9 h
= ?

Step 2: State the equation

Step 3: Fill in the equation with the quantities

= 100 km [E] ÷ 3.9 h
= 26 km/h [E]

Step 4: Give a written statement

The velocity of the plane is 26 km/h [E].

 

To calcluate Vav, it can follow the same procedures:

Average Velocity - Sample #1

A car was travelling due west (to the left), and after 40 minutes the car was 120 km from its starting location. What was the average velocity of the car during that particular trip?

Step 1: State the given information

= 120 km [W] or -120 km
t = 40 minutes = 2/3 h
= ?

Step 2: State the equation

Step 3: Fill in the equation with the quantities

= -120 km ÷ 2/3 h
= -180 km/h (or 180 km/h [W])

Step 4: Give a written statement

The average velocity of the car for that journey was -180 km/h or 180 km/h [W].

Average Velocity - Sample #2

A motorcycle is travelling with a velocity of 140 km/h [N] for 75 minutes, but then turns around and travels in the opposite direction at half the speed for 72 minutes. What is his average velocity throughout the entire trip?

Step 1: State the given information

= ?
t = ?
av = ?
1 = 140 km/h
2 = -70 km/h
t1 = 75 minutes = 1.25 h
t2 = 72 minutes = 1.2 h

Step 2: State the equation(s)

av = ÷ t
= (1 x t1) + (2 x t2)
t = t1 + t2

Step 3: Fill the equation(s) with quantities

t = 1.25 h + 1.2 h
t = 2.45 h

= (140 km/h x 1.25 h) + (-70 km/h x 1.2 h)
= 91 km

av = 91 km ÷ 2.45 h
av = 37 km/h

Step 4: Give a written statement

The average velocity of the motorcycle for the entire journey is 37 km/h.

Continue to the next lesson: ::Position-Time Graphs::