Question

A chipmunk, trying to cross a road, first moves \(80 \mathrm{cm}\) to the right, then \(30 \mathrm{cm}\) to the left, then \(90 \mathrm{cm}\) to the right, and finally \(310 \mathrm{cm}\) to the left. (a) What is the chipmunk's total displacement? (b) If the elapsed time was \(18 \mathrm{s},\) what was the chipmunk's average speed? (c) What was its average velocity?

Short answer

Answer: The chipmunk's total displacement is -1.70 m to the left, its average speed is 0.283 m/s, and its average velocity is -0.0944 m/s.

Step-by-step solution

Find the total distance traveled by the chipmunk

To find the total distance traveled by the chipmunk, we simply sum up all the distances it moved in each direction because distance is always positive. Total distance = 80 cm + 30 cm + 90 cm + 310 cm = 510 cm

Find the total displacement of the chipmunk

Displacement is a vector quantity. To find the total displacement, we can consider the rightward movement as positive and the leftward movement as negative, so we subtract the leftward movements from the rightward movements. Total displacement = (80 cm + 90 cm) - (30 cm + 310 cm) = 170 cm - 340 cm = -170 cm The displacement is negative, meaning the chipmunk is 170 cm to the left of its starting point.

Calculate the average speed of the chipmunk

To find the average speed, we can use the formula: Average speed = Total distance / Total time As given, the elapsed time is 18 seconds. Converting the total distance to meters, we get: 510 cm = 5.1 m So, the average speed is: Average speed = 5.10 m / 18 s = 0.283 m/s

Calculate the average velocity of the chipmunk

To find the average velocity, we can use the formula: Average velocity = Total displacement / Total time Converting the total displacement to meters, we get: -170 cm = -1.70 m So, the average velocity is: Average velocity = -1.70 m / 18 s = -0.0944 m/s

Final answers

(a) The chipmunk's total displacement is -170 cm or -1.70 m to the left. (b) The chipmunk's average speed is 0.283 m/s. (c) The chipmunk's average velocity is -0.0944 m/s.