Question

1. Analyze the number line above to describe the motion of the object. Be sure to include starting position, intermediate position, ending position, distance traveled, and displacement in your answer.
2. An object travels a distance of 6 meters in 2 seconds if average speed is found using the equation “ distance traveled/elapsed time” what is the average speed of the object? Be sure to include units in your answer.

3. An object has a displacement of +12 meters in six seconds. If average velocity is found using the equation “ change of position/elapsed time” what is the average velocity of the object? Be sure to include the correct sign and units in your answer.

Answer 1

1) Distance: 9 m, displacement: +5 m

2) The average speed is 3 m/s

3) The average velocity is +2 m/s

Explanation:

1)

We start by reminding the definitions of distance and displacement:

- Distance: it is the total length of the path covered by an object, regardless of the direction of motion

- Displacement: is the distance in a straight line between the initial position and final position of motion

Let's now analyze the motion represented in the figure:

Initial position: $x_0 = -1 m$

Intermediate position: $x_1 = +6 m$

Final position: $x_2 = +4 m$

Therefore, the distance covered is

$distance = |x_1-x_0|+|x_2-x_1|=|+6-(-1)|+|+4-(+6)|=7+2=9 m$

While the displacement is:

$displacement = x_2 - x_1 = +4 - (-1) = +5 m$

2)

The average speed is a scalar quantity defined as

$speed=\frac{d}{t}$

where

d is the distance travelled

t is the time taken

For the object in this problem,

d = 6 m

t = 2 s

Substituting, we find the average speed:

$speed = \frac{6 m}{2 s}=3 m/s$

3)

The average velocity is a vector quantity defined as

$velocity = \frac{d}{t}$

where

d is the displacement

t is the time interval

For the object in this problem,

d = +12 m

t = 6 s

Substituting, we find the average velocity:

$velocity=\frac{+12 m}{6s}=+2 m/s$

Where the positive sign + indicates the direction of the velocity vector.

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