Question

(1) use the diagram below to determine the average speed and velocity of the unicorn as she runs from point a to point b to point c and then to point d in 3 minutes.
(2) use the diagram below to determine the average speed and velocity of the woman as she walks from point a to point b and then to point c in 35 seconds.

Explanation:

Step1: Recall speed and velocity formulas

Speed = $\frac{\text{distance}}{\text{time}}$, Velocity = $\frac{\text{displacement}}{\text{time}}$

Step2: Calculate for the unicorn

• Distance from A - B - C - D: $d = 200 + 50+200 + 150=600$ m. Time $t = 3\times60 = 180$ s.
• Average speed: $v_{s}=\frac{d}{t}=\frac{600}{180}=\frac{10}{3}\approx3.33$ m/s.
• Displacement from A to D: $\Delta x=150$ m.
• Average velocity: $v_{v}=\frac{\Delta x}{t}=\frac{150}{180}=\frac{5}{6}\approx0.83$ m/s.

Step3: Calculate for the woman

• Distance from A - B - C: $d = 10+10 + 20=40$ m. Time $t = 35$ s.
• Average speed: $v_{s}=\frac{d}{t}=\frac{40}{35}=\frac{8}{7}\approx1.14$ m/s.
• Displacement from A to C: $\Delta x=- 20-(-10)= - 10$ m.
• Average velocity: $v_{v}=\frac{\Delta x}{t}=\frac{-10}{35}=-\frac{2}{7}\approx - 0.29$ m/s.

Answer:

Unicorn - Average speed: $\frac{10}{3}$ m/s, Average velocity: $\frac{5}{6}$ m/s
Woman - Average speed: $\frac{8}{7}$ m/s, Average velocity: $-\frac{2}{7}$ m/s