Question

1. define the equations for

a. speed
b. distance
c. time
d. velocity
e. average speed
f. acceleration
g. free fall velocity
h. free fall distance.

1. draw the speed/velocity triangle. explain how to use it.
2. give an example of units for.

a. speed and velocity
b. distance
c. time
d. acceleration

Explanation:

Step1: Recall speed formula

Speed is defined as the distance traveled per unit of time. The formula is $v = \frac{d}{t}$, where $v$ is speed, $d$ is distance and $t$ is time.

Step2: Recall distance formula

Distance is the product of speed and time. The formula is $d=v\times t$.

Step3: Recall time formula

Time is the distance divided by speed. The formula is $t = \frac{d}{v}$.

Step4: Recall velocity formula

Velocity is a vector - quantity and has the same formula as speed when considering magnitude only, $v=\frac{d}{t}$, but also includes direction.

Step5: Recall average - speed formula

Average speed is the total distance traveled divided by the total time taken. $\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$.

Step6: Recall acceleration formula

Acceleration is the rate of change of velocity. The formula is $a=\frac{v - u}{t}$, where $a$ is acceleration, $v$ is final velocity, $u$ is initial velocity and $t$ is time.

Step7: Recall free - fall velocity formula

For free - fall (assuming no air resistance and starting from rest), the velocity formula is $v = gt$, where $g$ is the acceleration due to gravity ($g\approx9.8\ m/s^{2}$ on Earth) and $t$ is the time of fall.

Step8: Recall free - fall distance formula

For free - fall (starting from rest), the distance formula is $d=\frac{1}{2}gt^{2}$, where $g$ is the acceleration due to gravity and $t$ is the time of fall.

For the speed/velocity triangle:
The speed/velocity triangle has three variables: speed ($v$), distance ($d$) and time ($t$). The triangle is divided into three sections with $v$ at the top, $d$ on the left and $t$ on the right. To use it, cover the variable you want to find. For example, if you want to find $d$, cover $d$ in the triangle. You are left with $v$ and $t$ side - by - side, so $d = v\times t$. If you want to find $v$, cover $v$ and you get $v=\frac{d}{t}$, and if you want to find $t$, cover $t$ and you get $t=\frac{d}{v}$.

For units:
a. An example of units for speed and velocity is meters per second ($m/s$).
b. An example of a unit for distance is the meter ($m$).
c. An example of a unit for time is the second ($s$).
d. An example of a unit for acceleration is meters per second squared ($m/s^{2}$).

Answer:

a. Speed formula: $v=\frac{d}{t}$; Distance formula: $d = v\times t$; Time formula: $t=\frac{d}{v}$; Velocity formula (magnitude): $v=\frac{d}{t}$; Average speed formula: $\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$; Acceleration formula: $a=\frac{v - u}{t}$; Free - fall velocity formula (starting from rest): $v = gt$; Free - fall distance formula (starting from rest): $d=\frac{1}{2}gt^{2}$
b. The speed/velocity triangle has $v$ at the top, $d$ on the left and $t$ on the right. Cover the variable you want to find to get the formula.
c. a. $m/s$; b. $m$; c. $s$; d. $m/s^{2}$