Question

speed:

1. what is the displacement between point a (3,5) and point b (8, 5)?
2. provide the equation to find speed:
3. use the speed equation to complete the table:

d =	t =	s =
200m		10m/sec
	10 seconds	200m/sec
100m	5 seconds
200m		20m/sec
100m	10 seconds
	20 seconds	15m/second

1. how far does a horse travel if its speed is 25km/h and it travels for 4 hours?
2. aunt minnie gives you $0.5 per second. how much money do you have after 8 seconds?
3. what is the difference between speed and velocity?

Explanation:

Step1: Calculate displacement between points

For two - dimensional points $A(x_1,y_1)$ and $B(x_2,y_2)$, the displacement formula is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 3,y_1 = 5,x_2 = 8,y_2 = 5$. So $d=\sqrt{(8 - 3)^2+(5 - 5)^2}=\sqrt{5^2+0^2}=5$.

Step2: Provide speed equation

The formula for speed is $s=\frac{d}{t}$, where $s$ is speed, $d$ is distance, and $t$ is time.

Step3: Complete the table

1. Given $t = 20$ s and $s=5$ m/s, using $d=s\times t$, we get $d = 5\times20=100$ m.
2. Given $d = 200$ m and $s = 10$ m/s, using $t=\frac{d}{s}$, we get $t=\frac{200}{10}=20$ s.
3. Given $t = 10$ s and $s = 200$ m/s, using $d=s\times t$, we get $d=200\times10 = 2000$ m.
4. Given $d = 100$ m and $t = 5$ s, $s=\frac{d}{t}=\frac{100}{5}=20$ m/s (already given).
5. Given $d = 200$ m and $s = 20$ m/s, using $t=\frac{d}{s}$, we get $t=\frac{200}{20}=10$ s.
6. Given $d = 100$ m and $t = 10$ s, $s=\frac{d}{t}=\frac{100}{10}=10$ m/s.
7. Given $t = 20$ s and $s = 15$ m/s, using $d=s\times t$, we get $d=15\times20 = 300$ m.

Step4: Calculate horse's travel distance

Given $s = 25$ km/h and $t = 4$ h, using $d=s\times t$, we get $d=25\times4=100$ km.

Step5: Calculate money received

Given the rate is $0.5$ dollars per second and $t = 8$ s, using $M=0.5\times t$ (where $M$ is money), we get $M=0.5\times8 = 4$ dollars.

Step6: Explain speed - velocity difference

Speed is a scalar quantity that only has magnitude (e.g., 5 m/s). Velocity is a vector quantity that has both magnitude and direction (e.g., 5 m/s to the east).

Answer:

1. 5
2. $s=\frac{d}{t}$

3.

$d$	$t$	$s$
200 m	20 s	10 m/s
2000 m	10 s	200 m/s
100 m	5 s	20 m/s
200 m	10 s	20 m/s
100 m	10 s	10 m/s
300 m	20 s	15 m/s

1. 100 km
2. 4 dollars
3. Speed is scalar, velocity is vector.