Question

(5) use the diagram below to determine the the average speed and velocity of the boy as he runs from point a to point b to point c and then to point d in 18 seconds.

Explanation:

Step1: Calculate total distance

Distance from A to B is $10 - (- 5)=15$ m, from B to D is $10 - 5 = 5$ m, from D to C is $5-0 = 5$ m. Total distance $d=15 + 5+5=25$ m.

Step2: Calculate displacement

Displacement is the straight - line distance from the starting point to the ending point. Starting at A(-5 m) and ending at C(0 m), displacement $\Delta x=0-(-5)=5$ m.

Step3: Calculate average speed

Average speed formula is $v_{avg - speed}=\frac{d}{t}$. Given $t = 18$ s and $d = 25$ m, so $v_{avg - speed}=\frac{25}{18}\text{ m/s}$.

Step4: Calculate average velocity

Average velocity formula is $v_{avg - velocity}=\frac{\Delta x}{t}$. Given $t = 18$ s and $\Delta x = 15$ m, so $v_{avg - velocity}=\frac{15}{18}=\frac{5}{6}\text{ m/s}$.

Answer:

Average speed: $\frac{25}{18}\text{ m/s}\approx1.39\text{ m/s}$, Average velocity: $\frac{15}{18}\text{ m/s}=\frac{5}{6}\text{ m/s}\approx0.83\text{ m/s}$