Question

round off your answer in 2 decimal point. include direction if needed. box your final answer
find
given
solution

1. what is the average speed and velocity of my bunny rabbit when she hops 6 meters to the east across the room in 11 seconds?
2. what is otters speed and velocity when it takes him 2 minutes to walk 100 meters north and another 1 minute to walk 70 meters to the west?
3. the boy travels to the church then to the mall. the first distance he covered is 150 m, north and the second distance is 150 m west. the boy covered the whole journey in 4 minutes.

a. what is the displacement covered by the boy?
b. find speed
c. find velocity

Explanation:

1.

Step1: Calculate average speed

Average speed is total distance divided by total time. Distance = 6 m, time = 11 s.
$v_{s}=\frac{d}{t}=\frac{6}{11}\approx0.55$ m/s

Step2: Calculate average velocity

Average velocity is displacement divided by time. Displacement = 6 m east, time = 11 s.
$v_{v}=\frac{\Delta x}{t}=\frac{6}{11}\approx0.55$ m/s east

Step1: Calculate total distance and total time

Total distance $d = 100 + 70=170$ m. Total time $t=2 + 1=3$ minutes = 180 s.

Step2: Calculate speed

$v_{s}=\frac{d}{t}=\frac{170}{180}\approx0.94$ m/s

Step3: Calculate displacement

Using Pythagorean theorem for displacement. $x = \sqrt{100^{2}+70^{2}}=\sqrt{10000 + 4900}=\sqrt{14900}\approx122.07$ m.
Direction $\theta=\tan^{- 1}(\frac{70}{100})\approx35.00^{\circ}$ west of north.

Step4: Calculate velocity

$v_{v}=\frac{\Delta x}{t}=\frac{122.07}{180}\approx0.68$ m/s, 35.00° west of north

Step1: Calculate displacement

Using Pythagorean theorem. Displacement $x=\sqrt{150^{2}+150^{2}}=\sqrt{2\times150^{2}} = 150\sqrt{2}\approx212.13$ m.
Direction $\theta = 45^{\circ}$ west of north.

Step2: Calculate total distance

Total distance $d=150 + 150 = 300$ m. Total time $t = 4$ minutes = 240 s.

Step3: Calculate speed

$v_{s}=\frac{d}{t}=\frac{300}{240}=1.25$ m/s

Step4: Calculate velocity

$v_{v}=\frac{\Delta x}{t}=\frac{212.13}{240}\approx0.88$ m/s, 45° west of north

Answer:

Average speed: 0.55 m/s
Average velocity: 0.55 m/s east

2.