Question

velocity: 8. provide the equation for acceleration. 9. use the acceleration triangle to complete the table: v = a . t | t = | a = | 20 seconds | 10 m/s/s | 50m/s | 25 seconds | 100m/s | 5m/s/s | 27km/h | 3 hours | km/h/h | 200m/s | 50 seconds | 40 seconds | 2m/s/s | 10 seconds | 10m/s/s

Explanation:

Step1: Recall acceleration formula

The formula for acceleration is $a=\frac{v - u}{t}$, where $a$ is acceleration, $v$ is final velocity, $u$ is initial velocity. When initial velocity $u = 0$, the formula simplifies to $v=a\times t$, and we can also get $t=\frac{v}{a}$ and $a=\frac{v}{t}$.

Step2: Fill the first row

Given $t = 20$ s and $a=10$ m/s², using $v=a\times t$, we have $v=10\times20 = 200$ m/s.

Step3: Fill the second row

Given $v = 50$ m/s and $t = 25$ s, using $a=\frac{v}{t}$, we get $a=\frac{50}{25}=2$ m/s².

Step4: Fill the third row

Given $v = 100$ m/s and $a = 5$ m/s², using $t=\frac{v}{a}$, we have $t=\frac{100}{5}=20$ s.

Step5: Fill the fourth row

Given $v = 27$ km/h and $t = 3$ h, using $a=\frac{v}{t}$, we get $a=\frac{27}{3}=9$ km/h².

Step6: Fill the fifth row

Given $v = 200$ m/s and $t = 50$ s, using $a=\frac{v}{t}$, we have $a=\frac{200}{50}=4$ m/s².

Step7: Fill the sixth row

Given $t = 40$ s and $a = 2$ m/s², using $v=a\times t$, we get $v=2\times40 = 80$ m/s.

Step8: Fill the seventh row

Given $t = 10$ s and $a = 10$ m/s², using $v=a\times t$, we have $v=10\times10=100$ m/s.

Answer:

$v=a\times t$	$t$	$a$
50 m/s	25 seconds	2 m/s²
100 m/s	20 seconds	5 m/s²
27 km/h	3 hours	9 km/h²
200 m/s	50 seconds	4 m/s²
80 m/s	40 seconds	2 m/s²
100 m/s	10 seconds	10 m/s²