Question

problem 5: an object travels 15 m east and 10 meters north in 12 seconds. what is the average speed of the object? what is the average velocity of the object? match the units of measurement with its description 1. 3 miles/hour south 2. 65 mph 3. 21 miles 4. 3 miles southwest a. velocity b. speed c. distance d. displacement

Explanation:

Step1: Calculate total distance

The object moves 15 m east and 10 m north. The total distance $d$ is the sum of the lengths of the paths it takes. So $d=15 + 10=25$ m.

Step2: Calculate average speed

The formula for average speed $v_{s}$ is $v_{s}=\frac{d}{t}$, where $t = 12$ s. So $v_{s}=\frac{25}{12}\approx2.08$ m/s.

Step3: Calculate displacement

The displacement $D$ is the straight - line distance from the starting point to the ending point. Using the Pythagorean theorem, $D=\sqrt{15^{2}+10^{2}}=\sqrt{225 + 100}=\sqrt{325}\approx18.03$ m.

Step4: Calculate average velocity

The formula for average velocity $v_{v}$ is $v_{v}=\frac{D}{t}$. So $v_{v}=\frac{\sqrt{325}}{12}\approx1.50$ m/s. The direction of the velocity is $\theta=\arctan(\frac{10}{15})\approx33.7^{\circ}$ north of east.

Step5: Match units

1. 3 miles/hour south is a velocity (A. velocity) since it has a magnitude (3 miles/hour) and a direction (south).
2. 65 mph is a speed (b. speed) as it only has a magnitude.
3. 21 miles is a distance (c. distance) as it is a scalar quantity representing length of path.
4. 3 miles southwest is a displacement (d. displacement) as it has a magnitude (3 miles) and a direction (southwest).

Answer:

Average speed: $\approx2.08$ m/s
Average velocity: $\approx1.50$ m/s at an angle of $\approx33.7^{\circ}$ north of east

1. A. velocity
2. b. speed
3. c. distance
4. d. displacement