Question

The graph below shows the position of an ant as it crawls over a flat picnic blanket. The total time for the ant to go from the start to the end position takes 1 minute and 45 seconds.


What is the average speed and average velocity of the ant?

A.) Average speed is 0.200 cm/s and average velocity is 0.0988 cm/s to the upper right.
B.) Average speed is 0.152 cm/s and average velocity is 0.910 cm/s to the upper right.
C.) Average speed is 0.975 cm/s and average velocity is 1.95 cm/s to the upper right.
D.) Average speed is 0.276 cm/s and average velocity is 0.136 cm/s to the upper right.

Answer 1

The average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.

The correct answer is option D.

In the given graph, we can deduce the following;

• the total time of the motion, = 1 mins + 45 s = 60 s + 45 s = 105 s

The average speed of the ant is calculated as;

$average \ speed = \frac{total \ distance }{total \ time }$

The total distance from the graph is calculated as follows;

• first horizontal distance from 2 cm to 8 cm = 8 - 2 = 6 cm

• first upward distance from 3 cm to 5 cm = 5 - 3 = 2 cm

• second horizontal distance from 8 cm to 6 cm = 8 - 6 = 2 cm

• second upward distance from 5 cm to 12 cm = 12 - 5 = 7 cm

• third horizontal distance from 6 cm to 13 cm = 13 - 6 = 7 cm

• fourth downward distance from 12 cm to 9 cm = 3 cm

• final horizontal distance from 13 cm to 15 cm = 2cm

The total distance = (6 + 2 + 2 + 7 + 7 + 3 + 2) cm = 29 cm

$average \ speed = \frac{total \ distance }{total \ time } = \frac{29 \ cm}{105 \ s} = 0.276 \ cm/s$

The average velocity is calculated as the change in displacement per change in time.

The displacement is the shortest distance between the start and end positions.

• This shortest distance is the straight line connecting the start and end position. Call this line P

• From the end position at x = 15 cm, draw a vertical line from y = 9 cm, to y = 3 cm. The displacement = 9 cm - 3 cm = 6 cm

• Also, draw a horizontal line from start at x = 2 cm to x = 15 cm. The displacement = 15 cm - 2 cm = 13 cm

Notice, you have a right triangle, now calculate the length of  line P.

                                                ↓end

                                                ↓

                                                ↓ 6cm

                                                ↓

  start -------------13 cm------------

Use Pythagoras theorem to solve for P.

$P^2 = 6^2 + 13^2\\\\P^2 = 36 + 169\\\\P^2 = 205\\\\P= \sqrt{205} \\\\P = 14.318 \ cm$

The average velocity of the ant is calculated as;

$average \ velocity= \frac{\Delta displacemnt }{total\ time }= \frac{14.318 \ cm}{105 \ s} = 0.136 \ cm/s$

Thus, the average speed of the ant is 0.276 cm/s and the average velocity is 0.136 cm/s.

Learn more here: https://brainly.com/question/589950