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Lab 7 Average speed and Average velocity

Concept 1: distance and displacement

Before learning about average speed and average velocity, it is important to understand the difference between distance and displacement.

Distance is a scalar quantity which generally implies how much ground has been covered by an object. On the other hand, displacement is a vector quantity, and it is the shortest possible distance between the start and end point. It does not follow the path you actually traveled. Instead, displacement is a straight line connecting where you started to where you finished. It only depends on the initial and final positions, not on any twists, turns, or curves along the way.

Distance vs. Displacement – Josh Emmanuel Alquiza's Writing Block

Let’s look at an example to better understand displacement. Imagine a girl running on a track. The distance she travels along the curved track from point A to point B is 200 m. However, the straight-line distance between point A and point B is only 50 m. So, her distance is 200 m, while her displacement is 50 m. If she continues running and completes one full lap of the track, the total distance traveled will be equal to the perimeter of the circle, but her displacement will be zero since she ends up at her starting point.

Concept 2: speed and velocity

Now, let us see what speed and velocity actually are.

Speed: Speed is a scalar quantity which means it has no direction. It denotes how fast an object is moving. If the speed of the particle is high it means the particle is moving fast and if it is low, it means the particle is moving slow.

Velocity: Velocity is a vector quantity, which means it has both magnitude and direction. It describes the rate at which an object changes its position. The direction of velocity is the same as the direction of motion of the object. Even if the object slows down and the magnitude of its velocity decreases, its direction remains the same as long as it continues moving in the same direction.

Concept 3: Average speed and Average velocity

Average Speed

The average speed of a body over a certain time interval is defined as the total distance covered divided by the total time taken. If a particle covers a distance between time and , then the average speed of the body is given by:

The general formula for average speed is:

Average Velocity

The average velocity of a body over a certain time interval is defined as the displacement of the body divided by the time taken. If a particle moves from point A to point B (displacement vector AB) between time and , then the average velocity of the particle is given by:

The general formula for average velocity is:

The video explains the concepts of average speed and velocity: https://www.youtube.com/watch?v=Z_mxLz5UZrI&t=43s

Exercise 1:

Imagine you walk 30 meters East and then 30 meters West to return to your starting point in 60 seconds. Show all calculations and include units.

What is your total distance? (10 points) (Hint: add all path lengths):

What is your total displacement (10 points) (Hint: consider starting point vs ending point)

What is your average speed (10 points) (Hint: use total distance ÷ total time)

What is your average velocity (10 points) (Hint: use displacement ÷ total time, include direction)

Exercise 2:

On the race track shown below: distance from A to B; B to C; C to D, are 100 meters. Starting from point A, a student jogged at a constant pace and recorded the times below.

	Time (s)
A to B	81.66
A to C	166.30
A to D	243.20
A to A	326.61

Show all calculations and include appropriate units for each answer.

The student’s average speed from B to C is (15 points)

The student’s average velocity from A to C is (15 points)

The student’s average speed for one full lap is (15 points)

The student’s average velocity for one full lap is (15 points)